Write down the value of angle x, y and z and give a reason for your answers: Angles
Answers
The missing angles and their reasons are as follows;
a) x = 65°; Opposite angles
b) y = 71°; Alternate angles
c) z = 44°; sum of angles in a triangle
What are the missing angles of the triangle?a) In triangles or line geometry, we know that the angles that are directly opposite to each other are known as opposite angles. They are also referred to as as vertical angles or even vertically opposite angles in some cases and are always congruent to each other.
We see that x is an opposite angle to 65 and so;
x = 65°
b) Alternate angles are gotten on the opposite sides of a transversal line they always have the same size. In this problem, we see that y is an alternate angle to 71° and as such;
y = 71°
c) The sum of angles in a triangle is 180° and as such;
x + y + z = 180°
Thus;
65 + 71 + z = 180
z = 180 - 136
z = 44°
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Related Questions
Estimate the amount of the tip by rounding the bill to the nearest ten dollars before calculating. 15% tip on a bill of $706.03 The amount of the tip is approximately
Answers
Answer: To estimate the tip, you can first round the bill to the nearest ten dollars. In this case, $706.03 rounded to the nearest ten dollars is $710.
Next, you can calculate the tip by multiplying the rounded bill amount by the tip percentage, 15% in this case.
15% of $710 is 15/100 * 710 = 106.50
So the amount of the tip is approximately 106.50
It's worth mentioning that this method of approximation is not always precise, but it can be a quick and easy way to calculate an estimate when you don't need a very precise answer.
Step-by-step explanation:
Which of the options below are the terms of the expression 5x² + 9x + 6? Choose all of the correct answers. 5x 9x 6 X x² 5 5x² 9
Answers
The terms of the expression are 5x², 9x and 6
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.
They are also known to be made up of arithmetic operation, such as;
DivisionAdditionParenthesesMultiplicationSubtractionBracket, etcIt is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.
They can be regrouped by the addition of their coefficients. Like terms are those that has the same variables to the same powers or coefficients.
The types are;
5x², 9x and 6
Thus, they are 5x², 9x and 6
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A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle.
A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n.
Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)
Step 2: m∠p − m∠o = 90 degrees (alternate interior angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
In which step did the student first make a mistake and how can it be corrected? (4 points)
a
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles)
b
Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles)
c
Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
d
Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Answers
Answer:
C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)
Step-by-step explanation:
The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)
Hope this helps
What is a polynomial class 7?
Answers
The polynomial which has a degree of 7 can be known as a polynomial of class 7.
Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.
The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.
Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.
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In the circle below, suppose m WXU= 102° and mLXWV=68°. Find the following.
Answers
In the circle below the suppose m WXU=102° and mL XWV=68° then the following is m ZXUV = 88°.
What is cyclic quadrilateral and explain the above answer?Four-sided shapes with all four corners on the same circle are known as cyclic quadrilaterals. A cyclic quadrilateral's internal angles are always added up to 360 degrees.
(a) m / WXU = 102° (Given)
(b) To find m ZXUV, we can use the property that the angles in a cyclic quadrilateral add up to 360°. Since WXU, XWV, and XLV are all inscribed angles that intercept the same arc, they are congruent. Therefore, m WXU = m XWV = m XLV = 102°. Adding these angles together, we have:
102° + 102° + 68° + m ZXUV = 360°
Solving for m ZXUV, we get:
m ZXUV = 360° - (102° + 102° + 68°)
m ZXUV = 88°
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This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A
BCDF
Frequency
5
10
15
3
2
Find the probability that a student earns a
grade of A, B, or C.
p=[?]
Enter a decimal rounded to the nearest hundredth.
Answers
Answer:
85.71% probability
Step-by-step explanation:
30 of 35 of the students are in abc range so take 35/100% or 0.35 and go 30/0.35 and you get 85.71%
Y=-1/2X+6 in standard form
Answers
The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.
How to find the definition of a linear function in standard form
In this question we find a linear function in slope-intercept form:
y = m · x + b
Where:
m - Slopeb - InterceptFrom which we must obtain the linear function in standard form:
a · x + b · y = c
Where:
a, b - Depedent coefficients.c - Independent coefficient.We can derive the standard form of the linear equation by algebra properties:
y = m · x + b
(1 / b) · y = (m / b) · x + 1
- (m / b) · x + (1 / b) · y = 1
If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:
- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1
(1 / 12) · x + (1 / 6) · y = 1
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PLEASE HELPPPP
(image below)
Answers
Answer:
b
Step-by-step explanation:
I think number B is the answer. because the square becomes root when it crosses the = . So, the answer is B
Answer:
b. ±√60
Step-by-step explanation:
You want to know the solution to x² = 60.
SolutionIn general, the process of solving for a variable's value requires you to "undo" what is done to the variable. This generally means you use inverse operations. The inverse of the squaring operation is the square root operation.
Taking the square root of both sides, we get ...
√(x²) = √60
|x| = √60 . . . . . . simplify the left side
x = ±√60 . . . . . . . write the equivalent without the absolute value bars
__
Additional comment
As with any operation performed on an equation, it must be done to both sides of the equal sign.
You will get a ±(radical) result whenever you take an even-index root: square root, fourth root, sixth root, and so on. Odd-index roots will have the same sign as the value under the radical.
√64 = ±8
∛64 = 4; ∛-64 = -4
After a long morning of sledding, Mrs. Fieldhouse made a batch of hot cocoa for her daughter and nighborhood friends. She divided it among 8 mugs. Each mug had more than 9 fluid ounces of hot cocoa. Write an inequality to describe the situation.
Answers
x>9 perfectly describes the situation.
In mathematics, inequalities characterise the connection between two non-equal numbers. Inequality implies being unequal. If two values are not equal, we use the "not equal symbol ()". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
Let x be the amount of hot cocoa in fluid ounces that each mug contains.
Since each mug has more than 9 fluid ounces of hot cocoa, we can write the inequality as:
x > 9
We also know that the total amount of hot cocoa made is 8 mugs * the amount of hot cocoa in each mug = 8x.
So the inequality can be written as:
8x > 9*8 = 72
or
x>9
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Pop is on sale at Save-U-Lots. Which pack has the lowest cost per unit?
A. 6- pack for $2. 49
B. 12-pack for $3. 99
C. 24-pack for $5. 49
Answers
In the case of a 24-pack for $5. 49, the cost of the unit is the lowest.
The cost per item is nothing to the amount of money invested in buying one item.
As we have 3 different scenarios:
Case A. 6- pack for $2. 49
As here. cost of 6 packs is $2.49, so for determining the cost of one pack we will divide $2.49 by 6.
So, the cost of 1 pack will be = 2.49/6 = 0.415 $/pack
B. 12-pack for $3. 99
As here. cost of 12 packs is $3.99, so for determining the cost of one pack we will divide $3.99 by 12.
So, the cost of 1 pack will be = 3.99/12 = 0.3325 $/pack
C. 24-pack for $5. 49
As here. cost of 24 packs is $4.49, so for determining the cost of one pack we will divide $5.49 by 24.
So, the cost of 1 pack will be = 5.49/6 = 0.22875 $/pack
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50PTS 50PTS 50PTS [D•O•N•T E•X•P•L•A•I•N]
Answers
Answer:x=20
Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get 8x+20 = 180, this can be simplified to 8x=160 or x = 20
Answer:
x = 20°
Step-by-step explanation:
Given angles,
→ 5x + 9
→ 3x + 11
Forming the equation,
→ (5x + 9) + (3x + 11) = 180°
{Because, sum of two angles in a straight line leads to 180°}
Now the value of x will be,
→ (5x + 9) + (3x + 11) = 180°
→ 5x + 3x + 9 + 11 = 180°
→ 8x + 20 = 180°
→ 8x = 180° - 20
→ x = 160/8
→ [ x = 20° ]
Hence, the value of x is 20°.
write a paragraph defending, refuting, or qualifying William Wordsworth's claim about the value of nature. Use a quote from one of his poems to support your claim OR present one of the quotes as a counterargument, if you are refuting his claim.
Answers
Answer: William Wordsworth, a prominent figure in the Romantic movement, believed that nature had an immense value and could have a profound impact on the human spirit. In his poem "I Wandered Lonely as a Cloud," he wrote, "Nature never did betray the heart that loved her," which is a claim that nature is a constant source of comfort and inspiration. In this poem he praises nature and its ability to be a source of beauty and joy.
One could argue that Wordsworth's claim is true based on the evidence that nature can have a positive impact on mental and physical health. Studies have shown that spending time in nature can reduce stress, improve mood, and boost overall well-being. Additionally, nature can be a source of inspiration for many artists and poets, including Wordsworth himself, who drew inspiration from the natural world for his poetry.
On the other hand, one could argue that Wordsworth's claim is idealistic and may not apply to everyone or every situation. Some people may not find nature as comforting or inspiring, especially those who live in urban areas with limited access to natural spaces. Additionally, there are negative impacts of human activities on nature, such as pollution and deforestation, which can make it harder for some people to find value in nature.
Overall, while Wordsworth's claim that "Nature never did betray the heart that loved her" is a strong statement, and it holds true for many people, but it's a personal perspective that may not apply to everyone. Each individual has their own relationship with nature and it's not always a constant source of comfort, however, it's a treasure that we should take care of, respect and appreciate in order to achieve a better quality of life.
Step-by-step explanation:
How do you know if a triangle is right acute or obtuse?
Answers
if a²+b²>c², the triangle is acute, if a²+b2²=c², the triangle is a right triangle, and if a²+b²<c², the triangle is obtuse.
where a and b are the lengths of the two shorter sides of the triangle and c is the length of the longest side.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.
An acute triangle has three angles that each measure less than 90°. In an acute-angled triangle, all three internal angles of the triangle are acute, that is, they measure less than 90°.
An obtuse triangle is a triangle with one angle that is greater than 90° degrees, it is not possible for a triangle to have more than one obtuse angle.
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Morgan bought 95 roses from the florist for her wedding. The roses cost $1.75 each, including sales tax. If Morgan gives the florist $200, how much change should she get back?
Answers
Answer:
33.75
Step-by-step explanation:
1.75*95 = 16 6.25
200 - 166.25 = 33.75
Question
A hot-air balloon is 1200 feet off the ground and its altitude is slowly changing at a constant rate of −712 feet per second.
How many seconds, s, will it take for the balloon to drop to below 310 feet?
Drag and drop a symbol and value to correctly complete the solution to this inequality.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
s Response area Response area
Answers
The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds
How to calculate the expression?To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.
Given the starting altitude of the balloon, we know:
h(0) = 1200 feet
The rate of change of the altitude, or the speed at which the altitude is changing, is given as:
dh/dt = −712 feet/second
This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:
h(t) = h(0) + dh/dt * t
We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:
310 = 1200 + (−712) * t
This equation can be solved for t by isolating t on one side and then dividing both sides by −712:
t = (1200 - 310) / −712
t = (890) / (−712)
t = 1.25 seconds.
So it will take 1.25 seconds for the balloon to drop below 310 feet.
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1. Length and breadth of a rectangular table-top are 36 cm and 24 cm respectively. Find its perimeter.
Answers
Answer:
120 cm.
Step-by-step explanation:
The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is
2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.
36-24=12 12/2=6
24+6=30
1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.
a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.
Incorrect but attempt was made (1 pt) Partially correct
(2-4 pts) Fully Correct
(5 pts)
b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.
Provided incorrect answer and no work shown (1 pt) Incorrect answer with work shown or Correct answer with no work shown
(2 pts) Correct with partial work shown (3-4 pts) Fully Correct with all work shown
(5 pts)
Answers
a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.
b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).
The cost per gallon of regular unleaded gas = $4.65
The cost of premium gas per gallon = $4.95
The total cost for gas = $874.80
Let gallons of regular unleaded gas = r
Let gallons of premium gas = p
Equation:4.65r + 4.95p = 874.8
If r = 87, the value of p is:
4.65(87) + 4.95p = 874.8
404.55 + 4.95p = 874.8
4.95p = 470.25
p = 95 gallons
Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.
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Can the sine ratio of an acute angle be greater than 1?
Answers
No, the sine ratio of an acute angle cannot be greater than 1. The sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio will always be less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's important to note that if you were to give an angle value greater than 90 degrees, the sine of the angle will be a negative value, but the ratio will still be less than one.
The sine ratio is a value between -1 and 1, and it is impossible for the sine of an acute angle to be greater than 1.
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What kind of triangle has 65 65 50?
Answers
Isosceles Triangle has 50°, 65°, 65°
An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.
Properties of Isosceles Triangle:
The two equal sides of an isosceles triangle are known as ‘legs’, and the angle between them is called the vertex angle or apex angle.In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The isosceles triangle has three acute angles, meaning that the angles are less than 90°.The sum of three angles of an isosceles triangle is always 180°. The side opposite the vertex angle is called the base and the base angles are equal, and perpendicular to the apex angle bisecting the base and the apex angle.To know more about Isosceles Triangle:
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Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
Answers
9x12
9x10=90
9x2=18
9x12=108
14x8
10x8=80
4x8=32
14x8=112
112+108=220
Answer:
$220
Step-by-step explanation:
first let's make the $12 bracelets as Type1 and the $8 bracelets as Type2,
then we calculate the amount she made by selling each type.
Eq.1 : No. of Type1 bracelets Selena made = 9
Amount she sold them for = $12
Amount she made by selling them = 9*12
= $108
Eq.2 : No. of Type2 bracelets Selena made = 14
Amount she sold them for = $8
Amount she made by selling them = 14*8
= $112
Now we calculate the Total Amount she made
we add both of the amounts
$108 + $112
= $220
Hope this helps :)
In the triangle below, the measure of angle G is 45 degrees, and the length of
HI = b cm. What is an expression for the length of HG?
Der b
G
I
H
45
Answers
The length of HG can be expressed as HG = b√2.
What is triangle?Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the most basic shapes in geometry and is found in nature in the form of mountains, icebergs and even the human face. It has a variety of applications in mathematics, engineering, and other fields. Triangles are also used to define angles and even the area of a plane.
This is because the triangle is a right triangle, and the Pythagorean Theorem states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Therefore,
HG2 = b2 + b2 = 2b2,
which reduces to HG = b√2.
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Please help I will give Brainiest answer
Answers
Answer: b
Step-by-step explanation:
4-3
——-
13.40- 10.05
= 1/3.35
=b
Therefore B is the correct answer.
Please mark brainliest I need three more!!!!!!!!!
How to determine if a triangle is right acute or obtuse based on side lengths calculator?
Answers
A triangle is said to be acute if the sum of the squares of its two shorter sides is greater than the square of its longest side.
How do you know if its right obtuse or acute?Less than 90 degree angles are considered acute. Right angles have a 90 degree angle. Angles that are obtuse exceed 90 degrees.
See samples of various angles and learn about them. If and only if side lengths a, b, and c satisfy a2 + b = c2, a right triangle will be formed. These numbers are referred to as a Pythagorean triple. When the square of a triangle's longest side equals the sum of the squares of its other two sides, the triangle is said to be a right triangle. So, in the ABC equation, if c2=a2+b2, then C is a right triangle, with PQR serving as the right angle.
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The amount of eroded rock is measured in cubic kilometers (km3). A cubic kilometer is a cube that measures 1 km on each side. How many km3 of rock were eroded
Answers
The amount of eroded rock in cubic kilometres is 1 km3.
To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.
In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:
20 m / 1000 = 0.02 km
Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:
10 km * 5 km * 0.02 km = 1 km3
So the amount of eroded rock in cubic kilometres is 1 km3.
Complete Question:
The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?
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The area of a sector of a circle is
18 pie cm². The radius of the circle is
6 cm. The angle in the sector is
Answers
Answer:
The angle in the sector is 180°.
Because the area of circle is 36 pie cm². So the angle is the half of 360°.
[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]
In the figure where 3x20 and 4x-36, which value of x will make aob, a traight line
Answers
The value of x that will make aob a straight line equation is x = -6.
To make aob a straight line, we need to make the gradients of both lines equal.
The gradient of the first line is 3x20 = 60.
The gradient of the second line is 4x-36 = 4x-36.
To make the gradients equal, we need to solve the equation 4x - 36 = 60.
Subtracting 36 from both sides gives us: 4x = 96.
Dividing both sides by 4 gives us x = -6.
Therefore, the value of x that will make aob a straight line is x = -6
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Please help me understand
Answers
The transformation is shifted up 2 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=-2x+3.
Here, the slope m of a line is -2 and y-intercept is 3
A) If the function g(x)=f(x)+k, where k=2.
Now, g(x)=-2x+3+2
g(x)=-2x+5
Here, the slope m of a line is -2 and y-intercept is 5
B) The slope of both functions are same
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Shifted up 2 units
Therefore, the transformation is shifted up 2 units.
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How do you graph 3 variable lines?
Answers
Three variable lines are drawn in the three dimensional coordinate system.
What is 3 dimensional coordinate plane?
Three-dimensional coordinate system is also called rectangular coordinate system. The system has three reference axes named X, Y and Z axis which are perpendicular to each other.
The above three axes intersect at the origin.
In the analytical geometry, location of each point is represented by three coordinate system. They give mathematical statement by using three-dimensional space.
How do we graph 3 variable lines?In order to plot in the three-dimensional plane, we need to determine the value of x, y and z. At first, we start from the origin and approach to the positive x direction if our x value is positive, otherwise we need to go to the negative x direction. After identifying the x coordinate, we need to move parallel to y direction and locate the y coordinate and finally we identify the z coordinate in the same way. In the last, we will join the points.
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Jason practiced making soccer goals and kept track of the results. he missed 3 goals but made 9 in one practice session. what can jason predict regarding goals made if his next practice session has 24 tries? jason will make 8 goals. jason will make 16 goals. jason will make 18 goals. jason will make 21 goals.
Answers
If Jason missed 3 goals and made 9 goals in one practice session the prediction we can make if the number of tries is 24 , then (c) Jason will make 18 goals .
Jason is practicing for making soccer goals and keeping a track of the results ;
the number of goals missed by Jason is = 3 goals ;
the number of goals that Jason made is = 9 goals ;
So , the total number of goals is = 12 goals ;
the ratio of making a goal to the total goals is = [tex]\frac{9}{12}[/tex] ;
So , the number of goals that Jason will make in 24 tries can be calculated as = [tex]\frac{9}{12} \times 24[/tex]
= [tex]9 \times 2[/tex]
= 18 .
Therefore , the Jason will make 18 goals in 24 tries .
The given question is incomplete , the complete question is
Jason practiced making soccer goals and kept track of the results. he missed 3 goals but made 9 in one practice session. What can Jason predict regarding goals made if his next practice session has 24 tries?
(a) Jason will make 8 goals.
(b) Jason will make 16 goals.
(c) Jason will make 18 goals.
(d) Jason will make 21 goals.
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Tom got a Mr. Potato Head for his birthday. It came with $3$ hairstyles, $2$ sets of eyebrows, $1$ pair of googly eyes, $2$ sets of ears, and $2$ sets of lips, a pair of regular shoes, and a bonus pair of clown shoes. If a complete Mr. Potato Head personality includes eyebrows, eyes, ears, lips, shoes and optionally hair, how many different wacky personalities can Tom come up with? Note that Mr. Potato Head can be bald. Note: You cannot "mix and match". For example, you cannot take the left eyebrow from one pair and the right eyebrow from the other pair.
Answers
Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.
Step-by-step explanation:
Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.
In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.