Christina has 46 baseballs and Spencer has 74 baseballs in their collections.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Christina and Spencer have 120 baseballs together.
Let christina has x baseballs
Spencer has 28 more
than Christina
x+28 has Spencer
So x+x+28=120
2x+28=120
Subtract 28 from both sides
2x=120-28
2x=92
Divide both sides by 2
x=46
Hence, Christina has 46 baseballs and Spencer has 46+28=74 baseballs in their collections.
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what is the answer to –87 × –9 =
Complete the paragraph proof.
We are given AB ≅ AE and BC ≅ DE. This means ABE is an isosceles triangle. Base angles in an isosceles triangle are congruent based on the isosceles triangle theorem, so ∠ABE ≅ ∠AEB. We can then determine △ABC ≅ △AED by
. Because of CPCTC, segment AC is congruent to segment
. Triangle ACD is an isosceles triangle based on the definition of isosceles triangle. Therefore, based on the isosceles triangle theorem, ∠ACD ≅ ∠ADC.
Angle ACD is congruent to angle ADC by transitive equality if angles 1 and 2 are both ACD because angle ACB is congruent to angle ADE in the step above. Therefore, angle 1 equals angle 2, as you can see.
What is isosceles triangle?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Here,
Given that segments AB and AE are congruent, the triangle ABE is required to be isosceles by definition.
As a result, angle ABC must be similar to angle AED, again in accordance with the definition of an isosceles triangle.
Consequently, triangle ABC must be congruent to triangle AED by SAS as you have been informed that segments BC and DE are congruent. Right now, it's unclear to you whether angle 1 is ACB or ACD.
Assuming it is ACB, CPCT shows that ACB is congruent to ADE. Angle 1 equals angle 2, so there you have it. Since angle ACB is supplementary to angle ACD and angle ADE is supplementary to angle ADC.
Since angle ACB is congruent to angle ADE from the step above, angle ACD is congruent to angle ADC by transitive equality if angle 1 and angle 2 are both ACD. Angle 1 equals angle 2, so there you have it.
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When constructing a perpendicular bisector of a segment, why should you make arcs with the same radius from each endpoint? Select the true statement.
The arcs with the same radius from each endpoint, C. make the intersection of the arcs equidistant from the endpoints
What is a parpendicular bisector?A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. Another line segment is split into two equal portions by a perpendicular bisector, which intersects it at a 90-degree angle.
The arcs with the same radius from each endpoint make the intersection of the arcs equidistant from the endpoints and we obtain a line segment that is perpendicular to the line segment from we take the measurement of arcs.
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Find an expression for the perimeter of the figure
The perimeter of the figure is 4d+6c - 6
How to calculate perimeter ?The distance around the outside of a 2D shape is known as its perimeter. Add together the lengths of all the sides to determine the perimeter.
We have been given a figure. We are asked to write an expression for the perimeter of our given figure.
We know that perimeter of a solid is sum of all of its side.
We can see that opposite side of our given figure are equal and our given figure is a rectangle.
We know that perimeter of rectangle is two times the length and width of rectangle, so the perimeter of our given figure would be:
2×(2d- 3+3c)
Use distributive property:
2 × 2d - 2 × 3 + 2 × 3 c
4d -6+6c
4d+6c-6
Therefore, the perimeter of our given figure is 4d+6c - 6
The complete question is : Write and simplify an expression for the perimeter of each figure
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The figure below is a rhombus.
x =[?]°
Answer:
X = 90°
Step-by-step explanation:
The figures cross sections form 4 90° angles.
A triangle has three angles which add up to 180°.Knowing x is a 90° angle we can do 180 - 90 to find out the other two angles (63 and z/y = 90).90 - 63 = 27.x = 90y = 27z = 27Ross made a scale drawing of his workshop as shown below. What is the actual width
of his workshop?
Answer:
43.2ft
Step-by-step explanation:
1in=10.8
4in=4*10.8
Width=4*10.8
Width=43.2
6. Danielle wants to construct different triangles with angle measures of
90°, 45°, and 45°, but she was only able to draw the triangle shown
at the right.
What mistake might Danielle have made?
Danielle didn't change the length of triangle then he draw that infinite triangles with given measure.
What is right triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles. it.
Given:
Danielle wants to construct different triangles with angle measures of
90°, 45°, and 45°. She was only able to draw the triangle shown at the right.
She did not consider that the triangle could be enlarged or reduced, while keeping the same angle measures, to make a different triangle.
Hence, Danielle didn't change the length of triangle then he draw that infinite triangles with given measure.
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A solid has volume 6 cubic units and surface area 22 square units. The solid is dilated, and the image has surface area 198 square units.
Answer:
162 units³
Step-by-step explanation:
Original solid:
V = 6 units³
SA = 22 units²
Dilated solid:
V = ?
SA = 198 units²
The ratio of the areas is 198/22 = 9
The ratio of the area is the square of the scale factor.
The scale factor is:
scale factor = √9 = 3
The ratio of the volumes is the cube of the scale factor.
ratio of volumes = 3³ = 27
The dilated volume is:
6 × 27 = 162 units³
Answer: 162 units³
Line segment cd is the perpendicular bisector of line segment ab. Is line segment ab the perpendicular bisector of line segment cd?.
Point E is closer to point A.
"I have added screenshot of the complete question as well as the
diagram"
What is line segment ?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie within those endpoints. The Euclidean distance between two endpoints of a line segment determines its length.
- In this diagram, line segment CD is the perpendicular bisector of line
segment AB
∴ AB ⊥ CD
∵ CD intersect AB at M
∴ M is the mid-point of AB
∴ The length of AM = the length of MB
- Assume the conjecture that the set of points equidistant from A
and B is the perpendicular bisector of AB is true
∴ Any point lies on the line CD equidistant from A and B
- If point E lies on the line CD
∵ CD is the perpendicular bisector of AB
∵ E lies on CD
∴ The length of EA = The length of EB
- From the figure point E is on the left side of the line CD
∵ Point A is on the left side of the line CD
∵ Point B is on the right side of the line CD
∵ Point E is on the left side of the line CD
∴ The length of AE < The length of BE
∴ Point E is closer to point A
Complete question: In this diagram, line segment CD is the
perpendicular bisector of line segment
AB. Assume the conjecture that the set of
points equidistant from A and B is the
perpendicular bisector of AB is true. Is
point E closer to point A, closer to point B,
or the same distance between the points?
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(1, 3) and (-3,-5)
Write a linear equation that passes through the given two points
Answer:
y = 2x + 1
1. Find the slope; (change in y values)/(change in x values)
Slope = (-5 - 3)/ (-3 - 1) = -8/-4 = 2
2. Find the y-intercept (b) using the slope intercept formula: y = mx + b
m = 2 and using point (1, 3) , solve for "b"
y = mx + b
3 = 2(1) + b
3 = 2 + b
1 = b
3. Write the linear equation: y = 2x + 1
Step-by-step explanation:
Rachel has 26 dimes. She is getting rolls of
dimes from the bank. She has enough money to get
up to 8 rolls of dime and each roll contains 50
dimes. The bank will not give partial rolls. The
function that models the number of dimes Rachel
will have after leaving the bank is f(r)=50r+26,
where r is the number of rolls of dimes she gets.
What is the practical domain of the function?
What is the practical domain of the function?
The practical domain of the function :
All integers from 1 to 8 and the set of f(r) is
f(r) = {76, 126, 176, 226, 276, 326, 376, 426}
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
Since Rachel has 26 dimes at the start, this would translate as the y-intercept. Or the value of y when x is zero. In this case, when she has no rolls of dimes., she would still have 26. Since each roll has 50 dimes. each, the function that models the number of dimes. Rachel will have is
f(r) = 50r + 26
If she can only afford 8 rolls, then the maximum number of dimes Rachel will have is:
f(8) = 50(8) + 26 = 426 dimes
The practical domain of the function :
all integers from 1 to 8
Substitute r=1 to 8 into the equation and find f(r).
{76, 126, 176, 226, 276, 326, 376, 426}
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.Solve for x
a) x = 192
b) x = 336
c) x = 8√3
d) x = 4√21
The value of x for the given Right angled triangle is x= 8√3. So, option c is correct.
What is meant by right-angled triangle?90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°. The bases and perpendiculars are the other two sides that are close to the right angle.
A right triangle is a triangle with one of the internal angles at 90 degrees. The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.
Given,
BD=28 and BC=12
CD=BD-BC
=28-12
=16
AB²=BC+AC²
AB²=(12)²+x²
x²=AB²-144 -----(1)
From ΔACD
AD²=AC²+CD²
AD²=x²+16²
x²=AD²-256 -----(2)
From ΔABD
BD²=AB²+AD²
784=AB²+AD²
2x²=AB²+AD²-144-256
2x²=784-144-256
2x²=384
x²=192
x=√192
x=√64×3
x=8√3
Therefore, The value of x for the given Right angled triangle is x= 8√3.
Hence, option c is correct.
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The length of the base of an isosceles triangle is x. The length of a leg is 3x - 2. The perimeter of the triangle is 66. Find x.
X= ?
Answer: x=5
Step-by-step explanation:
x=5 possibly i put diff numbers
When we reject the null and the null is true, we have a made a _________ __________.
When we reject the null hypothesis and the null hypothesis is true, we have made a Type I error.
What is a Hypothesis?In statistical hypothesis testing, the null hypothesis is a statement that represents the anticipated or "normal" outcome of a specific experiment. Unless there is evidence to the contrary, the null hypothesis, which is generally represented by the symbol "H0," is taken to be true.
A Type I mistake, sometimes known as a "false positive," arises when the null hypothesis is correct but is rejected based on the evidence. Applying a statistical test with a strong significance level increases the likelihood of rejecting the null hypothesis even when it is correct, which frequently leads to this mistake.
Making a Type I error can have major repercussions since it can result in judgments being formed based on flawed information and wrong inferences being drawn.
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Find the standard form of an equation where a=1, and the vertex is at (-1,11). Find the x and y intercepts and graph the equation.
Answer:
y = [tex]x^2+2x+12[/tex] (x and y intercepts under "Step-by-step explanation" section)
Step-by-step explanation:
We can start by finding the vertex form and then expand it to the standard form.
The vertex form of the quadratic equation is
[tex]y=a(x-h)^2+k[/tex], where a is a constant and (h, k) is the vertex.
By plugging in 1 for a, -1 for h, and 11 for k, we have:
[tex]y=1(x-(-1))^2+11\\y=(x+1)^2+11[/tex]
Now we simply expand this vertex form to get the standard form:
[tex]y = (x+1)^2+11\\y=(x+1)(x+1)+11\\y=x^2+x+x+1+11\\y=x^2+2x+12[/tex]
We can find the x and y-intercepts using the vertex form.
To find the x-intercept, we plug in 0 for y:
[tex]0=(x+1)^2+11\\-11=(x+1)^2\\\sqrt{-11}=x+1;-\sqrt{11}=x+1\\ x_{intercepts}:(-1+\sqrt{-11}, 0); (-1-\sqrt{-11})[/tex]
The x-intercepts are non-real answers, so the quadratic equation never intersects the x-axis.
To find the y-intercept, we plug in 0 for x:
[tex]y=(0+1)^2+11\\y=1^2+11\\y_{intercept} =(0,12)[/tex]
You have leased production space that is 275 ft x 200 ft. The property owner charges $5 per square foot to calculate the annual cost. How much is the annual cost?.
The annual cost is $275,000.
What is annual cost ?
Annual Costs refers to the sum of 1) Authorized Services for each Fiscal Year. 2) Administrative Costs; 3) any sums required to make up for actual or anticipated Special Tax Delinquencies for the current or preceding Fiscal Year.
The charge per square foot is $5.
The total square feet leased
=275ft x 200ft
=55,000 square ft.
The total cost of the annual rent is
=55,000 x $5
=$275,000
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a store has a 20% off sale on pants
The original price would typically be less expensive than the current price, though it is possible for the two to be equal in specific circumstances. The original price of the pants is $ 19
What was the original price of the pants?A store has 20% off sale on pants. With this discount, the price of one pair of pants before tax is $15.20.
n is the total price, 0.2n is the discount: n - 0.2n
n - 0.2n = 15.20
Step 2: Combine like terms
n - 0.2n = 15.20
0.8n = 15.20
Step 3: Divide both sides by 0.8
0.8n / 0.8 = 15.20 / 0.8
n = 19
$19 is the original price
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60 divided by 3 = g - 8 divided by 2 what does g equal?
Answer:
g = 48
Step-by-step explanation:
60/3 = g-8/2
20 = g-8/2
40 = g-8
g = 48
Answer:
g = 28
Step-by-step explanation:
60 ÷ 3 = g - 8 , that is
20 = g - 8 ( add 8 to both sides )
28 = g
Mark, taylor, & brian's ages are consecutive whole numbers. Mark is the youngest, and brian is the oldest. The sum of their ages is 111. How old is mark?.
The age of Mark, Taylor, & Brian's ages will be Whole numbers 36,37, and 38 respectively.
What exactly is a whole number?
Whole numbers are a collection of positive integers and zero that do not contain any fractions.
It is denoted by the letter "W," and its corresponding set of numbers are "0," "1, 2, 3,,","5,,"6,,"7,","8,"..."
It is given that Mark, Taylor, & Brian's ages are consecutive whole numbers, Mark is the youngest, and Brian is the oldest and the sum of their ages is 111.
Suppose the age of mark is x as a result the age of Taylor and brian will be x + 1 and x + 2 respectively.
From the given condition the sum of their ages is 111,
⇒x + x + 1 + x + 2 = 111
⇒3x + 3 = 111
⇒3x = 111 - 3
⇒3x = 108
⇒x = 108/3
⇒x = 36
The age of Mark, x =36
Age of Taylor, x+1 = 36+1 =37
Age of Brian, x+2 =36+2=38
Thus, if their age is in consecutive whole numbers. The age of Mark, Taylor, & Brian's ages will be 36,37, and 38 respectively.
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Jordan and hi children went into a grocery tore and he bought $13. 50 worth of apple and mango. Each apple cot $1. 50 and each mango cot $0. 75. He bought 6 more mango than apple. Determine the number of apple and the number of mango that Jordan bought
By solving equations, we know that the number of apples and mangoes purchased is 8 and 2, respectively.
What are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal.
Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the word "equal" separating them.
So, we know that:
Apple and mango are worth $13.50.
Each mango costs $0.75, but each apple costs $1.50.
Let the number of apples be x and the number of mangoes be y, so that:
1.50x + 0.75y = 13.50
Fewer apples than mangoes by six That is to say,
x = y + 6
x - y = 6
The two resulting equations are:
1.50x + 0.75y = 13.50
x - y = 6
The simultaneous equation's solution provides
x = 8
y = 2
Therefore, by solving equations, we know that the number of apples and mangoes purchased is 8 and 2, respectively.
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Which of the following equations describes the graph shown below?
(1) y = log5 x
(3) y = log, x
(2) y = log₂ x
(4) y = log₁ x
The graph shown in the question is representing the equation y = log x, so option 3 is correct.
What is a graph?A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
Given:
The graph is shown in the image,
Put the value of x and y from the graph to the equation as shown below,
x = 1, y = 0
Put in option 1,
y = log5 x
0 = log5
0 = 0.69
Again, put in option 2,
y = log x
0 = log1
0 = 0
Hence, it is the correct option.
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A moving company has one large truck for furniture and one small truck for boxes.During one move, it took the large truck 4 hours to travel 180 miles. It took the small truck 3 hours to make the same trip.How much faster did the small truck travel in miles per house.?
Answer:
15
Step-by-step explanation:
180 / 4 = 45
180 / 3 = 60
Answer: 15
Step-by-step explanation:
A baker bought 15 kg of flour. He used 3 1/2 kg to make one cake and 2 1/4 kg to make another. How much flour has he used in all? How much was left?
Answer: He used 5 3/4 kg in all. There was 9 1/4 kg left.
Step-by-step explanation:
Add 3 1/2 and 2 1/4 to find how much he used. The common denominator is 4 so convert 3 1/2 to 3 2/4. Then add. The answer will be 5 3/4.
Subtract 5 3/4 from 15 to get how much is left. The answer will be 9 1/4.
a professor teaches a class of 42 students. if only 34 students show up to take the first exam, then how would we characterize this group who took the first exam?
Correct this group constitutes a sample of all students in the class.
What are some instances of intuitive reasoning?
As an illustration, when we enter a coffee shop, we immediately recognize a cup as one that we have seen many times before.
We also immediately recognize that it will probably be hot and spill quickly over an uneven surface.
What is the intuitional method?
Intuition is the earliest means of knowing. When we use our intuition, we are putting our trust in our feelings, emotions, and/or instincts to lead the way.
When using intuition, one believes what seems true rather than looking at the facts or using reason.
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A 7.5 hg bag of bananas costs 35 Swedish krona ( money ) . If the cost is proportional, how much would 1 kg bag of bananas cost
Answer:
Step-by-step explanation:
First of all we do conversion.
We have 7.5hg which equals to 0.075kg or 75grams.
Then we use direct proportion where if one value increases so does the other which in this case is the weight of the item is directly proportional to the price of it. Therefor we get this.
Weight Money
75(grams) 35(Swedish Krona)|
1000(grams) x
We cross mutiply.
35,000 divided by 75
so x = 466.67 Swdish Krona
(I Think)
Let’s say that Charlotte wants to have money left over after buying the concert ticket. Complete the statement to write an inequality that represents Charlotte having money left over after buying the ticket.
The inequality that represents Charlotte having money left over after buying the ticket. is
8m + 20 < 68
What is inequality?Inequality is a means of representing the relationship existing between the left hand side and right hand side of equations, using other terms aside exactly using only "equal to"
Having left over means that the the cost of the ticket should be less than the amount Charlotte has
Therefore, 8m + 20 should be less than 68 and this represented by
8m + 20 < 68
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Rectangle jklm is similar to rectangle wxyz . what is the scale factor of a dilation from jklm to wxyz ? enter your answer as a decimal in the box.
If the rectangle JKLM is similar to rectangle WXYZ , then the scale factor is 1.5 .
In the question ,
two rectangle figures are given ,
the rectangles JKLM and WXYZ are similar ,
So , to find the scale we consider the ratio of the sides of the rectangle .
the ratio of the sides is ⇒ ZW/JM = WX/JK
Substituting the values of ZW = 13.5 , JM = 9 , WX = 18 and JK = 12 ,
we get ,
13.5/9 = 18/12
⇒ 1.5 = 1.5
So , the rectangles are similar and the scale factor is = 1.5 .
Therefore , the scale factor is 1.5 .
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A couch is on sale for $81.60, which is 24% off the original price
What’s the original price?
Answer: It should be $101.18
Step-by-step explanation:
You would basically subtract the 81.60 to the 24% making it 19.58. then from the 19.58 you add the 81.60 and there you go!
Write and solve an equation that represents the following math sentence.
Twenty-six equals the sum of 13.5 and the quotient of a number and 2.5.
26 equals 13.5 plus m over 2.5; m = 5
26 equals 13.5 plus m over 2.5; m = 31.25
26 = 13.5 + 2.5m; m = 5
26 = 13.5 + 2.5m; m = 31.25
The equation is 26 = 13.5 + 2.5 m, and the value of m is 5, so option C is correct.
What is equation?Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way.
Given:
Twenty-six equals the sum of [tex]13.5[/tex] And the quotient of a number and [tex]2.5.[/tex]
Write the equation in mathematical form,
26 = 13.5 + quotient × 2.5
Assume the quotient is m then,
26 = 13.5 + 2.5 m,
Solve the equation to get the value of m,
26 - 13.5 = 2.5 m,
m = 5
Therefore, the equation is 26 = 13.5 + 2.5 m, and the value of m is 5.
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Alicia has 9 paintings she wants to hang side by side on her wall.
(a) in how many ways can she arrange all 9 paintings? show your work
(b) if she only wants to display 5 of the paintings, in how many ways can she choose the paintings she wishes to display show your work.
(c) in how many ways can she arrange 5 out of 9 paintings? Show your work.
a) The number of ways that she can arrange the 9 paintings is; 362880 ways
b) If she only wants to display 5 of the paintings, the number of ways can she choose the paintings she wishes to display is; 126
c) The number of ways can she arrange 5 out of 9 paintings is; 120
How to solve probability combinations?a) If we take 9 paintings to be hung in 9 spaces arranged side by side, then it means that the first space can have any one of the 9 paintings, the second space can have any one of the remaining 8 paintings (as 1 is already hung), the third space can have any one of the remaining 7 paintings (as 2 already hung) e.t.c
Thus;
Number of ways to arrange all the paintings from left to right = 9! = 362880
b) We are now told that she only wants to display 5 of the paintings. Thus;
Number of ways she can choose the paintings she wishes to display is done by the combination formula;
nCr = n!/(r!(n - r)!)
9C5 = 9!/(5!(9 - 5)!)
= 126 ways
c) Any 5 of the 9 paintings can be arranged in;
5! = 120 ways
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