The integers are 71 and 72 respectively
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.
They are also known to be composed of mathematical operations such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcFrom the information given , we have;
x + 1 + x + 2 = 143
collect like terms
2x = 143 - 3
Subtract like terms
2x = 140
Make 'x' the subject
x = 140/2
x = 70
The numbers are;
x + 1 = 70 + 1 = 71
x + 2 = 70 + 2 = 72
Hence, the numbers are 71 and 72
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Write an expression describing all the angles that are coterminal with 346°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)
______ degrees
Answer:
346 + 360k
You can get coterminal angles by adding intervals of 360 degrees
please help me out thanks
A non-zero matrix A with A² = 0 is A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex].
We need to find a 2 x 2 non- zero matrix with A² = [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
A² = A x A
If A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex], then A x A = [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}a^2+bc&ab+bd\\ac+dc&bc+d^2\end{array}\right][/tex]
This is called matrix multiplication.
Now consider the matrixes of the form A = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]
Then A² = [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
Also Consider a matrix A = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]
Then A² = [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] x [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
So any matrix of the form [tex]\left[\begin{array}{cc}0&x\\0&0\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}0&0\\x&0\end{array}\right][/tex] with x any number, will give A² = 0
In particular, A = [tex]\left[\begin{array}{cc}0&1\\0&0\end{array}\right][/tex] is a non-zero matrix with A² = 0.
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If F(X) = 5x-7 and G(X)= -2x+9, what is G(F(X))?O A. -10x +23O B. -10X2 +59x-63O C. -10x+38O 10XD. 10x7 - 59x+63
f(x) = 5x - 7
g(x) = -2x + 9
g(f(x)) = -2(5x -7) + 9 = -10x + 14 + 9 = -10x + 23
g(f(x)) = -10x + 23
Answer:
Option A: -10x + 23
How many 2-liter bottles of soda will you need to fill ten 500 milliliter containers?1. 4 2. 2 3. 3 4. 1 How many milliliters are 1/5 liter?1. 5002. 2003. 1004. 50
Hello there. To solve this question, we have to remember some properties about conversion of values.
1. How many 2-liter bottles of soda will you need to fill ten 500 mililiter containers?
First, multiply the number of containers by its capacity, that is
[tex]10\cdot500=5000\text{ mililiters}[/tex]Notice that 1000 mililiters is equivalent to 1 liter, hence
[tex]5000\text{ mililiters }=5\text{ liters}[/tex]To fill these containers with 2-liter bottles of soda, you'll need at least 3 bottles.
The answer to the first question is 3.
2. How many mililiter are 1/5 liter?
Considering 1 liter = 1000 mililiters, we have that
[tex]\dfrac{1}{5}\text{ liter }=\dfrac{1}{5}\cdot1000\text{ mililiters }=200\text{ mililiter}[/tex]Hence the answer to this question is 2. 200
without graphing, describe the transformation of each parabola or absolute value function y = 2 |x|+ 1
Remember the following transformations of a function:
[tex]c\cdot f(x)[/tex]This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0
If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1
[tex]f(x)+c[/tex]This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.
Therefore, starting with the absolute value function:
[tex]\lvert x\rvert[/tex]Multiply the function by 2:
[tex]2\cdot\lvert x\rvert[/tex]Since 2>1, then this is a vertical stretching by a factor of 2.
Next, add 1:
[tex]2\cdot\lvert x\rvert+1[/tex]This will translate the stretched absolute value function one unit upwards.
Therefore, the complete description of the transfromation would be:
[tex]y=2\cdot\lvert x\rvert+1[/tex]Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.
The owners of the Movie Palace use the Illuminator 100 light bulb in their projectors, but are now considering switching to the Illuminator 100 Plus, a more powerful light bulb that projects movies onto larger screens farther away. The Illuminator 100 Plus projects movies onto screens 108 feet wide and 180 feet from the projector, while the Illuminator 100 projects movies onto screens only 81 feet wide, as shown in the figure below. How much farther from the projector, in feet, is the screen for the Illuminator 100 Plus than the screen for the Illuminator 100 ?
Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;
Illuminator 100 plus bulb
It movies onto screens ;
108 ft wide
180 ft away from the projector
Illuminator 100 bulb
81 ft wide
? : from the projector
Here apply the idea of similarity ratios where;
The ratio
the mean absolute
for the following set of Determine
deviation
data: 1, 1, 3, 5, 5, 6, 8, 11
The mean absolute deviation is 2.5.
What is Mean Absolute Deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.
How to calculate the mean deviation from the mean:
Calculate the mean of the provided observations.Determine how much each observation differs from the estimated mean.Analyze the mean of the differences discovered in step two.Given data:1, 1, 3, 5, 5, 6, 8, 11
So, mean of the data is
= 1+ 1 +3 +5 +5+ 6+ 8 +11 / 8
= 40 /8=
5
Now, Mean absolute deviation is
= | 1-5| + |1-5| + |3-5 | + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|/ 8
= 4 + 4 + 2+ 0 + 0+ 1 + 3 +6 /8
= 20/8
=2.5
Hence, the mean absolute deviation is is 2.5.
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When given a line of 3x + 6y = 8, how do you find slope intercept?
The line is given by 3x + 6y = 8
To find the slope and the y-intercept, we must rewrite the equation in the form y = ax + b, where a is the slope and b is the y-intercept.
The first step is subtract 3x from both sides of the equation:
3x + 6y - 3x = -3x + 8
6y = -3x + 8
Then, we divide both sides by 6:
6y/6 = (-3x + 8)/6
y = -x/2 + 4/3
Therefore, the slope is -1/2 and the y-intercept is 4/3
While sailing a boat offshore, Bobby sees a lighthouse and calculates thatthe angle of elevation to the top of the lighthouse is 3°. When she sails her boat700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.How tall, to the nearest tenth of a meter, is the lighthouse?
Given
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
To find:
How tall, to the nearest tenth of a meter, is the lighthouse?
Explanation:
It is given that,
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
That implies,
[tex]\tan3\degree=\frac{y}{x+700}[/tex]Also,
[tex]\begin{gathered} \tan5\degree=\frac{y}{x} \\ y=x\tan5\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \tan3\degree=\frac{x\tan5\degree}{x+700} \\ (x+700)\tan3\degree=x\tan5\degree \\ x\tan3\degree+700\tan3\degree=x\tan5\degree \\ (\tan5\degree-\tan3\degree)x=700\tan3\degree \\ 0.0351x=36.6854 \\ x=1045.7m \end{gathered}[/tex]Then,
[tex]\begin{gathered} \tan5\degree=\frac{y}{1045.7} \\ y=1045.7\tan5\degree \\ y=91.5m \end{gathered}[/tex]Hence, the height of the light house is, 91.5m.
I'm In K12" Help me Pleeasee *I Will Give "Brainlyest to The First Person"
The correct inequality sign for the first number expression is > and for the second number, the expression is <.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The mixed fractions are:
-19 5/6 = -119/6 = -19.83
-20 1/6 = -121/6 = -20.166
-19 5/6 > -20 1/6
|-19 5/6| = |-119/6| = 19.83
|-20 1/6| = |-121/6| = 20.166
|-19 5/6| < |-20 1/6|
Thus, the correct inequality sign for the first number expression is > and for the second number, the expression is <.
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A fair die is rolled 4 times. What is the probability of having no 1 and no 3 among the rolls? Round your answer to three decimal places.
Answer:
Step-by-step explanation:
You have to assume each roll is independent. The probability of rolling a fair die is 1/6. When you roll the die, you only care about 2,4,5, and 6 since you do not want to get 1 or 3. So the probability is of getting a 2,4,5 and 6 is 4/6.
You could of also see it as the probability of NOT getting a 1 or 3 is:
[tex]1-\frac{2}{6} =\frac{4}{6}=\frac{2}{3}[/tex]
Now you roll the die 4 times with each success being 2/3
[tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} =(\frac{2}{3})^4=.197530864[/tex]
C IS BETWEEN A AND D, B IS THE MIDPOINT OF AC . IF BD =15 AND BC= 7, FIND AD
BD= 12
BC=7
Is this from a graded quiz?
1. Line Q goes through (-6,7) and (4,-2). Write the equation of line Q.
First, find the slope of the line using the slope formula:
Provided two points (a,A) and (b,B) on a line, its slope is given by:
[tex]m=\frac{A-B}{a-b}[/tex]For the points (-6,7) and (4,-2), we have:
[tex]\begin{gathered} m=\frac{7--2}{-6-4} \\ =\frac{7+2}{-10} \\ =\frac{9}{-10} \\ \therefore m=-\frac{9}{10} \end{gathered}[/tex]The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):
[tex]\begin{gathered} 7=-\frac{9}{10}(-6)+b \\ \Rightarrow7=\frac{54}{10}+b \\ \Rightarrow b=7-\frac{54}{10} \\ \therefore b=\frac{8}{5} \end{gathered}[/tex]Substitute b=8/5 and m=-9/10 to find the equation of line Q:
[tex]y=-\frac{9}{10}x+\frac{8}{5}[/tex]2(3x - 1) + 2(4x + 5) = 8
Answer:
0
Step-by-step explanation:
2(3x -1) + 2(4x + 5) = 8 Distribute the 2's
2(3x) + 2(-1) + 2(4x) + 2(5) = 8
6x - 2 + 8x +10 = 8 Combine like terms
14x + 8 = 8 Subtract 8 from both sides of the equaion
14x = 0 Divide both sides by 14
x = 0
please help with this practice question, thank you
A map state where your friend lives have a scale 1/2 inch: 10 miles.
Your friend measured the distance between her town and the state capital on the map. Her measurements were 4 1/2 inches. Based on your friend's measurement, what is the actual distance in miles between her town and the state capital?
The actual distance is 90 miles between the town and the state capital based on the scale of the map
1/2 inch on the map = 10 miles
So, 1 inch = 20 miles
Distance between the town and state capital = 4 1/2 inches
The mathematical relationship between a small unit of measurement on a map, such as an inch or centimetre, and the corresponding real-world unit of distance, such as a kilometre or a mile, is known as a map scale.
The actual distance in miles between the town and the state capital is given by:
Distance between town and state capital* Scale of the map
= 4.5*20
= 90 miles
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Calculate the perimeter for each of the following
a) Perimeter = 17.4 cm
b) Perimeter =210.6 cm
How are the perimeters calculated?
a) The perimeter of an irregular polygon = Sum of all the sides of the polygon.
Converting value of all sides to centimetres.
Perimeter = 3.4 +3.2 +4.3 +3.7+2.8
= 17.4 cm
b) The perimeter of an irregular polygon = Sum of all the sides of the polygon.
Converting value of all sides to centimetres.
Perimeter = 29.1+25.3+30+28.6+32.6+36.5+28.5
=210.6 cm
What is the perimeter of a polygon?
The total length of a polygon's boundary is what is referred to as its perimeter. To put it another way, a polygon's perimeter is equal to the sum of its sides. Due to the fact that polygons are closed plane shapes, their perimeters likewise reside in a two-dimensional plane.If the lengths of the sides of a polygon are known, it is possible to determine its area and perimeter.To learn more about perimeter of a polygon, refer:
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Im not the best at word problems please help.Frank knows that his first four test grades were 74, 76, 77, and 84. Use the formula x‾=x1+x2+…+xnn to find Frank's grade on the fifth test if his test average is 80.6.
Given:
Frank knows that his first four test grades were 74, 76, 77, and 84
We will find Frank's grade on the fifth test if his test average is 80.6.
So, let the fifth grade = x,
The average is the sum of the grades over the number of the grades
So,
[tex]\frac{74+76+77+84+x}{5}=80.6[/tex]Solve the expression to find x:
[tex]\begin{gathered} 74+76+77+84+x=5\cdot80.6 \\ 311+x=403 \\ x=403-311=92 \end{gathered}[/tex]So, the answer will be: the fifth grade = 92
Maggie's brother is 3 years younger than four times her age. The sum of their ages is 42.How old is Maggie?Maggie isyears old.
The age of Maggie is 9 years and her brother whose age 3 years less than four times Maggie's age is 33 years old.
What is age?
Age is the difference in days, months, and years between the day, month, and year of birth and the day, month, and year of the event, expressed in the largest completed unit of solar time, such as years for adults and children and months, weeks, days, hours, or minutes of life, as appropriate, for infants under one year of age (Gregorian calendar).
Let the ages of Maggie and her brother be X and Y.
There are two condition given in the question through which we can form a system of equation containing two equations.
First condition: The sum of their ages is 42.
Therefore,
X + Y = 42
Second Condition: Maggie's brother is 3 years younger than four times her age.
Therefore,
4X - 3 = Y
We get the system of equation:
X + Y = 42
4X - 3 = Y
Solving this system of equation
4X - 3 = Y
4X - 3 = 42 - X
X = 45/5
X = 9
Putting the value of X in one of the equation:
Y = 42 - X
Y = 42 - 9
Y = 33
Therefore, age of Maggie is 9 years and age of her brother is 33 years.
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Look at triangle ABC on the coordinate plane. 1 Which coordinate plane shows triangle ABC after a reflection over the y-axis?
We a figure is being reflected over the y-axis, the y-coordinates of its point will not change. However, the x-coordinates will be multiplied by -1.
Given points of the figure:
Point A: -5,-2
Point B: -4,-4
Point C: -6,-4
Let's now determine the new points of the figure once reflected over the y-axis.
Point A: -5,-2 ➜ Point A': (-5)(-1),-2 = 5,-2
Point B: -4,-4 ➜ Point B': (-4)(-1),-4 = 4,-2
Point C: -6,-4 ➜ Point C': (-6)(-1),-4 = 7,-4
Looking at the
State the domain and range for the graph and tell if it is a function.
The arrows indicate that the graph of the function continues beyond what can be seen in the image.
Notice that the graph does not appear to have asymptotes; then, the domain of the function is:
[tex]\text{domain}=(-\infty,\infty)[/tex]And the range is:
[tex]\text{range}=(-\infty,\infty)[/tex]Since the graph seems to continue towards the +y-direction and the -y-direction
Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; the graph is a function.
please help me solve,the question is A cylinder with a diameter of 8 feet is cut out of a cube that measures 8 feet on each side.What is the volume of the resulting shape? ( use Pi and round to the nearest tenth.) ______ ft3
Side of cube = 8 ft
Volume of cube = Side x Side x Side
Volume of cube = 8 x 8 x 8
Volume of cube = 512 feet^3
A cylinder with diameter 8feet is cute form the cube
Height of cylinder = Side of cube
Height of cylinder = 8 feet
Diameter of cylinder = 8 feet
Radius of cylinder = 4feet
[tex]\begin{gathered} \text{Volume of cylinder =}\Pi\times radius^2\times Height \\ \text{Volume of cylinder =}\Pi\times4\times4\times8 \\ \text{Volume of cylinder =}401.92ft^3 \end{gathered}[/tex]The volume of resulting shape = Volume of cube - Volume of cylinder
Volume of resulting shape = 512 - 401.92
Volume of resulting shape = 110.08 ft^3
Answer: 110.08 ft^3
50 points for this one
Answer:
-1, 0
Step-by-step explanation:
Hello!
We can test each solution for by substituting the value for x, and see if the inequality is true.
x = -1:[tex]\frac{3(-1)^2}{(-1)^2+3} < 1[/tex][tex]\frac34 < 1[/tex]This inequality is true.
x = -2:[tex]\frac{3(-2)^2}{(-2)^2+3} < 1[/tex][tex]\frac{12}{7} < 1[/tex]This inequality is not true because 12/7 is greater than 1.
x = 0:[tex]\frac{3(0)^2}{(0)^2+3} < 1[/tex][tex]0 < 1[/tex]This is inequality is true.
x = 3:[tex]\frac{3(3)^2}{(3)^2+3} < 1[/tex][tex]\frac{27}{12} < 1[/tex]This inequality is not true because 27/12 is greater than 1.
The solutions that work are -1 and 0.
Answer: A
Step-by-step explanation:
I need help with this practice problem solving• I believe the subject is complex numbers and vectors I will send an additional picture that goes along with this, it is a graph, use the graph to answer this
Solution
a + b = (-2, -1)
Using Parallelogram method
HELP ASAP WILL GET THE BRAINLEST FOR THIS ANSWER PLEASE ANSWER CORRECTLY
Answer:
(x,y)->(x+4,y-5)
Step-by-step explanation:
Find a set of common points first, for example, A and A', or B and B'
Then, find the coordinates of the two points. I'm choosing B and B'.
B: (1,8) x = 1, y = 8
B':(5,3) x = 5, y = 3
from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct
Which of the following is not a solution 3x-5<2
SIMPLIFY THE EQUALITY FIRST
[tex]3x \leqslant - 2 + 5 \\ 3x \leqslant 3 \\ \frac{3x}{3} \leqslant \frac{3}{3} \\ x \leqslant 1[/tex]
X CAN BE ALL THE NUMBERS LESS OR EQUAL TO 1
IN THE PICTURE THE ONLY OPTION THAT CONTRAST THE INEQUALITY IS OPTION B BECAUSE IT IS GREATER THAN 1.
HOPE THIS HELPS
Answer:
option B
Step-by-step explanation:
3x - 5 ≤ -2
add 5 to both sides
3x - 5 + 5 ≤ -2 + 5
3x ≤ 3
divided both sided by 3 to get x alone
3x/3 ≤ 3/3
x ≤ 1
option B is the only choice that is above 1.01 making it not a solution
Write a mathematical expression for the following statement
Four times x is more than 13
Answer:
4x>13
Step-by-step explanation:
4 × X=4x
>=more than symbol
what is 1 trillion to the thenth power? .. .. ..
[tex]\sf{}[/tex]
1 trillion to the tenth power is (10¹⁴)¹⁰ or (10¹³)¹⁰.
What is a trillion?1,000,000,000,000One trillion is equal to one million million, or 1,000,000,000,000, and on the short scale, we write this as 1012. (ten to the twelfth power). This number is now commonly referred to as one trillion because it is a thousand times bigger than the short-scale billion.We need to determine how many crores one trillion represents. Therefore, by dividing one trillion by one crore, we can find the solution to the puzzle. As a result, we discover that 100000 = 1000000000000/10000000. As a result, we learn that $1 trillion is equivalent to 100,000 Indian Rupees.So, 1 trillion to the tenth power:
1 trillion to the tenth power = (10¹⁴)¹⁰ or (10¹³)¹⁰Therefore, 1 trillion to the tenth power is (10¹⁴)¹⁰ or (10¹³)¹⁰.
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the probability that the mean salary of the sample is less than $60,000 is? round 4 decimals if needed.
Answer:
0.26599
Step-by-step explanation:
We will assume a normal distribution for the salaries
We have the following information
Mean μ = 64000
Standard deviation σ = 6400
And we are asked to find P(X < 60000)
First find the z score corresponding to X = 60000
The z score is given by (X - μ) / σ
z score for 60000 with μ = 64000 and σ = 6400 is
z = (60000 - 64000)/6400
z = -40000/6400 = -0.625
We can either look up the P value from the z-tables or simply use a calculator
P(X < 60000) and this works out to 0.26599
I only need help with part "b." I have provided the answer for "a" to help.
Part b.
If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:
Factor of 3
[tex]3\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {3} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Multiply:
[tex]\begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix}[/tex]Answer:
[tex]\begin{equation*} \begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix} \end{equation*}[/tex]