Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
2 ( [tex]\frac{1}{4}[/tex] )²
= 2 × [tex]\frac{1}{16}[/tex] ← cancel 2 and 16 by 2
= 1 × [tex]\frac{1}{8}[/tex]
= [tex]\frac{1}{8}[/tex]
If a ⊥ y and x ∥ y, then _____
Answer:
x⊥a
Step-by-step explanation:
If we draw this out, we see that x is perpendicular to a as well.
A circus is composed of acrobats, ballerinas, clowns, and dogs. The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Twice the combined number of acrobats and ballerinas is five more than three times the number of clowns. If the number of dogs is one more than the number of clowns, how many people and animals belong to the circus
If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.
Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.
We have to find total people and animals belong to the circus.
An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.
let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.
According to given information in question the equations are:
x+ y-z=u-1-----------------------1
2(x+ y)=3z+5-------------------2
u=z+1----------------------------3
Put the value of u from 3 in 1
x+y- z=z+1-1
x+y-2z=0
from 2
z=2x+2y-5/3
put the value of z in x+y-2z=0
x+y-2(2x+2y-5/3)=0
-x-y+10=0
x+ y=10-------------------------4
put put the value of x+y=10 in 1
10-z=u-1
u+z=11-----------------------------5
solving 3
u-z=1------------------------6
Now add 5&6
u+z+u-z=11+12
2u=12
u=6
Put the value of u in 6
6-z=1
z=5
From above we get x+y=10, u=6, z=5
Add all three we get the total number of people and animals belong to circus.
x+y+u+z=10+6+5
=21
Hence there are total 21 people and animals belong to the circus.
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Michael is renting a bicycle for $12 per hour.
Which of the following is equivalent to this rate?
a.)
20 cents per minute
b.)
14 cents per minute
c.)
5 cents per minute
d.)
7 cents per minute
Answer:
20 cents/minute
Step-by-step explanation:
We need to convert both units
1 dollar is 100 cents
12 dollars * 100 cents/1 dollar = 1200 cents
1 hour = 60 minutes
1 hours * 60 minutes / 1 hour = 60 minutes
12 dollars/ hour = 1200 cents / 60 minutes
Simplify
20 cents/minute
Answer: A. 20 cents per minute
Unit rate given: $12 per hour
Conversion:
$1 = 100 cents
$12 = 1200 cents
1 hour = 60 minutes
Solving steps:
amount in cents/time in minutes = 1200/60 = 20 cents per minute
Circle Q is centered at the origin. Is point (-5, 0) on the circle? Justify your answer
Answer: D
Step-by-step explanation: I just took the quiz
If r= 1 and 0=3.14/4, what is the approximate arc length?
=
A. 1.047 units
B. 0.524 units
C. 0.785 units
D. 1.571 units
The approximate arc length from the task content is; Choice C; 0.785 units.
What is the approximate arc length?Since the arc length is given mathematically by the formular;
Arc length = (A/360) × 2πr
Hence, since A = π/4 = 18/4 = 45.
Hence; Arc Length = (45/360) × 2 × 3.14 ×1
Arc length = 6.28/8 = 0.785 units.
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How many sides would there be in a convex polygon if the sum of all but one of its interior angles is $1070^{\circ}$
As Convex polygon:
A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The
Convex Polygon:
A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.
Lets simplify the given problem,
If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:
1070 =[n - 2] x 180, where n = number of sides
[tex]1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180[/tex]
n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.
Hence the number of sides is 8
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30 points and mark brainlest
A rectangular picture has dimensions 3 inches by 2 inches. Find the dimensions of the pictures if it has to be enlarged with a scale factor of 5. Question 18 options: 15 inches × 10 inches 3 5 inches × 2 5 inches 8 inches × 7 inches 12 inches × 8 inches
The dimensions of the enlarged rectangular picture is 15 x 10 inches.
What are the dimensions of the enlarged rectangular picture ?When the dimensions of the enlarged rectangular picture is enlarged by a scale factor of 5, it means that the dimensions would be five times larger what they were initially.
New dimensions : (3 x 5) x (2 x 5)
15 x 10 inches
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Answer:
I’m just adding so you can mark brainliest
Step-by-step explanation:
Suppose that x and y vary inversely, and x = 12 when y = 8 . Write the function that models the inverse variation.
Answer:
[tex]y=\frac{96}{x}[/tex]
Step-by-step explanation:
So when x and y, vary inversely, it means that the product of x and y will remain constant such that: [tex]xy=c[/tex]. This means that the function can be defined as [tex]y=\frac{c}{x}[/tex] by dividing both sides by x. In this case x=12, and y=8, this means the constant is equal to 12 * 8 which is 96. So we have the equation: [tex]xy = 96[/tex], which can be defined as [tex]y=\frac{96}{x}[/tex]
In circle O, R_T and S_U are diameters
Applying the vertical angles theorem, the measure of VU is determined as: 64°.
What is the Vertical Angles Theorem?If two angles lie directly opposite each other, they are vertical nagles and are therefore equal.
13x = 15x - 8 [vertical angles theorem]
13x - 15x = - 8
-2x = -8
x = 4
Let y represent m(VU). Since m(RV) = m(VU), therefore:
13x + 2y = 180 [angles on a straight line]
Plug in the value of x
13(4) + 2y = 180
52 + 2y = 180
2y = 180 - 52
2y = 128
y = 64°
m(VU) = 64°.
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If I have 8$and I buy something 3$ how many change wil I get?
Answer:
5$
Step-by-step explanation:
it is 5 because the difference of 8 and 3 is 5
Which expression is equivalent to 14 times 14?
2 squared
2 Superscript 14
14 squared
14 Superscript 14
Answer:
[tex]14^{2}[/tex]
Step-by-step explanation:
14*14
14 is the base. We are multiplying 14 two times. Two would be the exponent
14 ^2
Flying against the wind, an airplane travels 6230 kilometers in 7 hours. flying with the wind, the same plane travels 10,480 kilometers in 8 hours. what is the rate of the plane in still air and what is the rate of the wind?
The speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.
We assume the speed (rate) of the plane in still air to be x kilometers per hour, and the speed (rate) of the wind to be y kilometers per hour.
Thus, flying against the wind, the acting speed (rate) for the plane will be x - y kilometers per hour.
Flying with the wind, the acting speed (rate) for the plane will be x + y kilometers per hour.
We are given that flying against the wind, the airplane travels 6230 kilometers in 7 hours.
Thus, speed (rate) = 6230/7 kilometers per hour = 890 kilometers per hour.
Equating this to the derived speed of the airplane flying against the wind, we get x - y = 890 ... (i).
We are given that flying with the wind, the airplane travels 10480 kilometers in 8 hours.
Thus, speed (rate) = 10480/8 kilometers per hour = 1310 kilometers per hour.
Equating this to the derived speed of the airplane flying with the wind, we get x + y = 1310 ... (i).
Now, on adding equations (i) and (ii), we get:
2x = 2200,
or, x = 1100.
Substituting x = 1100 in (ii), we get:
x + y = 1310,
or, 1100 + y = 1310,
or, y = 1310 - 1100 = 210.
Thus, the speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.
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ext → Post Test: Systems of Linear Equations and Inequalities
1
Use the drawing tool(s) to form the correct answers on the provided graph.
1
Graph the system of equations given below on the provided graph.
2x - 3y = -18
3x + y = -5
Then, use the Mark Feature tool to plot the solution to the system.
The way to construct the equation in a graph is illustrated.
How to illustrate the information?Converting the equation in slope-intercept form
2x-3y= -18
-3y= -2x-18
-3y= -(2x+18)
3y=2x+18
y=(2x+18)/3
And for equation 2
y= -5-3x
The points can be calculated by putting negative and positive values of x in both equations.
The graph is attached as a picture.
As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.
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Complete the input-output table for linear function y=3x
The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the linear function y = 3x:
When x = -2; y = 3(-2) = -6
When x = -1; y = 3(-1) = -3
When x = 0; y = 3(0) = 0
When x = 1; y = 3(1) = 3
When x = 2; y = 3(2) = 6
The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).
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Answer: ( -6/ 6/ 9
Step-by-step explanation:
I need a helping hand!
Answer:
x = 145°
Step-by-step explanation:
x and 35° are a linear pair and sum to 180° , that is
x + 35° = 180° (subtract 35° from both sides )
x = 145°
You buy 12 packages of discounted socks for a total cost of $85.50, which includes a 5% discount.
Before the discount, how much did a single package of socks cost?
a.)
$7.50
b.)
$4.75
c.)
$6.78
d.)
$10.68
Answer:
a) $7.50
Step-by-step explanation:
The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?
[tex].95x = 85.50[/tex]
[tex]x = 90[/tex]
So the original price is $90. Divide this by 12, obtaining $7.50.
Answer:
a)$7.5
Step-by-step explanation:
Solution:
Let X represents socks
Given,
Selling price (SP) of 12x=$85.50
Discount precent (d%)=5%
So,
SP=(100-d)% of MP. [this formula really exist believe it or not]
85.50= (100-5)/100 ×MP
or, 85.50×100 =95×MP
or, 8550/95=MP
So,MP=$90
Now At last ,
cost of 1 shocks before discount is 90/12
which is $7.50 ans√
The triathletes were offered water as they rode by the volunteer station. The volunteers handed them cones with the dimensions shown. If each triathlete sloshed 1/3 of the water out before they drank it, how many cubic cm of water did they slosh out? Round to the nearest tenth.
Height 7cm
radius 3.5cm
The slosh-out water is 29.9 cubic cm.
What is volume?Volume is defined as the space covered by any solid body in the three-dimensional plane. For the cylinder, the parameters are height and radius.
The volume of the cone is calculated as:-
V = ⅓r^2h
V = ⅓r^2h
V = ⅓(3.5)^2(7)
V = ⅓(12.25)(7)
V = 1/3(85.75)
V = 85.75/3
1/3 cup of water is sloshed out:
Sloshed water = (85.75/3 )/3
Sloshed water = 29.9 cubic cm
Therefore, the sloshed-out water is 29.9 cubic cm.
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Simplify the ratio. 2 1/2: 3 1/3
Answer:
two and a half to three and one third
Step-by-step explanation:
A
Ф
Ф
center of triangle ABC.
30° R
15
в
What is m/QOB?
0000
30°
60°
75°
90°
Answer:
757575757575757575757575757575757575757575751) The dimensions of an irregular solid are as shown in the figure below.
a) Write a polynomial function, in standard form, to model the volume of this solid.
b) If the volume of the solid is 208 cubic inches, what is the value of x?
Hello,
a) Volume of the figure = Volume of light blue rectangular parallelepiped - volume of dark blue rectangular parallelepiped
Volume of rectangular parallelepiped = lengh × high × height
Volume of light blue rectangular parallelepiped :
V = (x + 2) × (x + 5) × (2x + 1)
V = (x² + 5x + 2x + 10) × (2x + 1)
V = (x² + 7x + 10) × (2x + 1)
V = 2x³ + 15x² + 27x + 10
Volume of dark blue rectangular parallelepiped :
V = x × 3 × (x + 5)
V = 3x(x + 5)
V = 3x² + 15x
Polynomial function, in standard form, to model the volume of this solid :
V = 2x³ + 15x² + 27x + 10 - (3x² + 15x)
V = 2x³ + 15x² - 3x² + 27x - 15x + 10
V = 2x³ + 12x² + 12x + 10
b) We have to solve 2x³ + 12x² + 12x + 10 = 208
⇔ 2x³ + 12x² + 12x - 198 = 0
⇔ 2(x - 3)(x² + 9x + 33) = 0
⇔ x = 3 or x² + 9x + 33 = 0
a = 1 ; b = 9 ; c = 33
Δ = b² - 4ac = 9² - 4 × 1 × 33 = -51 < 0 ⇔ Δ < 0 ⇒ no solution
So if the volume of the solid is 208 cubic inches, the value of x is 3
Triangles J K L and M N R are shown.
In the diagram, KL ≅ NR and JL ≅ MR. What additional information is needed to show ΔJKL ≅ ΔMNR by SAS?
∠J ≅ ∠M
∠L ≅ ∠R
∠K ≅ ∠N
∠R ≅ ∠K
The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.
Here we are given that
KL = NR
JL = MR
Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.
So for the triangles to be congruent by SAS, angle L must be congruent to angle R.
∠L=∠R
Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.
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Answer:
B
Step-by-step explanation:
L=R
PLEASE HELP
Select the correct answer.
Which statement is true about this function for all values of x<4
A) The function is negative
B) The function is decreasing
C) The function is positive
D) the function is increasing
Answer: B) The function is decreasing
Step-by-step explanation:
As x increases, y decreases.
Alexandra needs to reshingle her roof. She leans a ladder against the the wall of the house so that the top of the ladder is 8 feet above the ground. The bottom of the ladder is 5 feet from the base of the wall. Find the angle formed between the ladder and the house. Round the answer to the nearest whole degree. A. B. C. D. Please select the best answer from the choices provided A B C D
If the top is 8 feet above the ground and ladder is 5 feet away from bottom of wall then the angle between ladder and house is 58°.
Given top is 8 feet above the ground, ladder is 5 feet away from bottom of the wall.
Trigonometric ratios are the ratios of the sides of a right angled triangle. sin is the ratio of perpendicular and hypotenuse , cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is the ratio of hypotenuse and perpendicular, sec is the ratio of hypotenuse and base, cot is the ratio of base and perpendicular.
Here we use tan d where d is the angle between ladder and wall of the house.
tan d= P/B
tan d=8/5
tan d=1.6
[tex]d=tan^{-1} 1.6[/tex]
d=57.99
After rounding off it will be 58°.
Hence the angle between ladder and house is 58°.
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Using the markings in the following image, answer the questions below:
a. Determine whether group A or group B (or both) show a pair of similar triangles or not. Tell how you know this.
b. For the group(s) with similar triangles, calculate all unknown side lengths. If possible, calculate the unknown angles. Explain your answers.
c. For the group(s) with similar triangles, calculate the scale factor. What is the relationship of the area of the original figure to the area of the translated figure? Explain.
d. For the group(s) with similar triangles, tell (roughly) what transformations would be needed to make one of the triangles carry onto the other triangle in its group.
The two triangles in group A are similar because two angles of one are congruent to two angles of the other.
How to explain the triangle?The two triangles in group A are similar because two angles of one are congruent to two angles of the other.
The two triangles in group B are not similar. The ratio of the short sides of the two triangles is 10:4 or 2.5:1, and that is the same ratio as the two sides 24 and 9.6.
However, using the fact that an angle bisector in a triangle divides the opposite side into two segments in the same ratio as the lengths of the two sides that include the angle, the length of the third side of the left triangle can be found to be about 25.12; and 9.25 times 2.5 is not close to 25.12.
b. In group A, the third side of the first triangle, by the Pythagorean Theorem, is sqrt(306).
The scale factor between the two triangles is 3:5, so the length of the third side of the second triangle is 15*(5/3) = 25.
In both triangles, the third angle measure is 31 degrees, since the sum of the three angles is 180.
c. The scale factor, again, is 3:5 which means the ratio of the areas of the two triangles is 3²:5² or 9:25.
d. The first triangle can be carried onto the second with the following transformations:
(1) dilate by a factor of 5/3 to make it the same size;
(2) rotate 90 degrees counterclockwise;
(3) translate so the hypotenuses of the two triangles are the same line segment; and
(4) reflect on the hypotenuse.
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A car travels 24 km between 9:30 am and 10:15 am. What is its average speed in km/h?
Answer:
32 km / hr
Step-by-step explanation:
930 to 1015 is 45 min = .75 hr
24 km / .75 hr = 32 km /hr
here is the histogram of a data distribution. all class widths are 1. which of the following is the closest to the mean of this ditribution
In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?
The simplest way to factor polynomials is to use the greatest common factor.
How to illustrate the polynomial?It should be noted that the polynomial simply means the expression of more than two algebraic terms.
In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.
Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.
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Which of the following could represent the interval −4 ≤ x ≤ 6?
Answer:
Step-by-step explanation:
-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6
x = {-4,-3,-2,-1,0,1,2,3,4,5,6}
Hope I helped...
D
A fabric mill produces 4953 metres of fabric in a day. How much fabric will it
365 days]
produce in a year? [1 year =365 days
The fabric mill produce 1,807,845 meters of fabric in 365 days.
A fabric mill produces 4953 meters of fabric in a day.
What is simplification?operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.
We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845
Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.
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Question 3 (Essay Worth 10 points)
(05.07 MC)
The scatter plot shows the number of strawberries that have been picked on the farm during the month of February:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Strawberries and the x axis is labeled Days in February
Part A: Using computer software, a correlation coefficient of r = 0.01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm. (5
It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated
How to illustrate the information?1. Part A:
Since the points in the scatter plot shows a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.
The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to 1.
Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with a negative slope.
r = + 1 is a perfect positive correlation: the points will adjust perfectly to a line with a positive slope.
r = 0 means that the variables are not correlated at all.
Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows another thing.
Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.
2. Part B.
A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.
Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.
Thus, the scenario could be:
Amount of rainfall in mm (x) Number of strawberries picked (y)
100 20
50 40
25 80
12.5 160
6.25 320
The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.
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