Angle CBE and angle BED are alternative interior angles. It means that they have the same measure, so:
\(\begin{gathered} \angle BED=\angle CBE \\ \angle BED=135\text{ \degree} \end{gathered}\)Answer: 135°
A manufacturer claims that a particular automobile model will get 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine believe that this claim is high and plan a test with a simple random sample of 25 cars. What should the researchers conclude if the sample mean is 49 miles per gallon with standard deviation 2.3 miles per gallon
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Given values:
\(The \ population\ mean(\bar{x})=50\\\\The \ sample \ mean, \mu =49\\\\standard \ deviation, \sigma =2.3\\\\ (n)=25\\\\null, H_o :\ \mu=50\\\\alternate, H_1 :\ \mu<50\\\\ testing \ the \ statistic (t) = \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt(n)}}\\\\to = \frac{49-50}{\frac{2.3}{\sqrt{25}}}\\\\to =-2.1739\\\\| to | =2.1739\\\\p-value\ :left \ tail - H_a : (p < -2.1739 )=0.0199\\\\null, H_o: \ \mu=50\\\\alternate, H_1: \ \mu<50\\\\test \ statistic: \ -2.1739\\\\p-value: 0.0199 \sim 0.02\\\\\)
Therefore, the 0.02 p-value is sufficient proof to reject the claim form of the manufacturer.
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
(Picture)
Answer:
(B) y = f(x - 3) is the answer.
please thanks and follow me.
Answer:
BE careful check that this is the right question for you this one is b there is another that looks similar that is a
Step-by-step explanation:
a rectangular garden has dimensions of 5 feet by 12 feet. if the length and width of the garden are increased by the same amount, and the resulting area is 144 square feet, how much was each side increased?
Based on the data, we can infer that the difference in length after the garden increment is 4 feet on each side.
How to find how much the garden increased in length and width?To find how much the garden increased in length and width we must carry out the following procedure:
First of all we must calculate the area of the garden:
side * side = area5 * 12 = 60According to this result we know that the increase is more than half in the values. Therefore, we can add 3 or more feet to each side and recalculate the area of the garden.
5 + 3 = 812 + 3 = 158 * 15 = 120In this case we add 3 feet to each side and calculate the area that would give these side measurements 8 and 15. The area would be 120, you still wouldn't have enough length on the sides to have an area of 144.
5 + 4 = 912 + 4 = 1616 * 9 = 144In this case we add 4 feet on each side and calculate the area that would be given with these side measurements 9 and 16. The area would be 144, it would be the measurement mentioned in the statement.
Based on the above, we can infer that the rise is 4 feet on each side.
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18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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A rectangle with a perimeter of 40 inches has a width that is 3 times the length. What is the length And the width
The Length is 5 inches and the Breadth is 15 inches
What is Perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.
Solution:
Perimeter of Rectangle = 2*(Length + Breadth)
According to the question
Breadth = 3*Length
Perimeter = 40
40 = 2*(Length + 3*Length)
20 = 4*Length
Length = 5 inch
Breadth = 15 inch
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The diagram shows a right-angled triangle.
24 cm
18 cm
_Not to scale
Calculate the value oft. Give your answer correct to 1 decimal place.
Answer:
can i have a photo, please?
Step-by-step explanation:
Which number(s) below belong to the solution set of the equation? Check all that apply.
x + 10 = 40
A. 40
B. 80
C. 400
D. 4
E. 30
F. 50
Answer:
E only
Step-by-step explanation:
can anyone help me ?
Answer:
Table 3.
Step-by-step explanation:
Evaluate the root without using a calculator, or note that the root isn't a real number.
9514 1404 393
Answer:
A. 2
Step-by-step explanation:
When you don't know if a number like 256 is a power of anything, it can work reasonably well to start by simply dividing by the factors you know.
256/2 = 128128/2 = 6464/2 = 3232/2 = 1616 = 2^4, so 256 = 2^4 · 2 · 2 · 2 · 2 = 2^8The 8th root of 2^8 is 2, choice A.
what is 11/4 times 4/9
Answer: 11/9
Step-by-step explanation:
you would cross out the two 4s(using butterfly method) and make them 1s. So 11 x 1 and 1 x 9 = 11/9
Answer:
11/4 times 4/9 is 11/9
Step-by-step explanation:
We have to find,
(11/4) times 4/9
\((11/4)(4/9) = (11*4/4*9)\)
We can cancel the 4s from the numeratorand denominator to get,
\((11*4/4*9) = (11*1/1*9) = 11/9\\=11/9\)
The answer is 11/9
Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range.
f(x) =x^2 +12x+6
What is the vertex?
What are the x-intercepts?
What is the y-intercept?
what is the axis of symmetry?
Identify the function's domain
Identify the function's range.
The Vertex is : (-6, -30)
The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)
The Y-intercept is : (0, 6)
The Axis of symmetry is : x = -6
The functions Domain: is All real numbers
The Range is : All real numbers greater than or equal to -30.
To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.
To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)
In this case, a = 1, b = 12, and c = 6.
Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.
To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)
So, the vertex is (-6, -30).
To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)
Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.
Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).
The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)
Thus, the y-intercept is (0, 6).
The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.
The domain of the function is all real numbers since there are no restrictions on the possible input values of x.
To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.
Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).
As a result, the range of the function is all real numbers greater than or equal to -30.
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Martha is a writer. She earns three and one‐half cents for each word written. Each day, she writes a five‐hundred‐word article for the local newspaper. How much does she earn for each article?
Answer:
Step-by-step explanation:
Simple
Money she earns for an article = 3 1/2 x 500 = 1750
16
Select the correct answer.
Which of the following graphs shows the solution set for the inequality below?
Ix+21+7>10
OA HH
OB. H
5
1 0 1 2 3
0 1
2 3 4
10
5 6
The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.
Option D is the correct answer.
We have,
We need to isolate the absolute value |x + 2| on one side of the inequality.
We subtract 7 from both sides.
|x + 2| > 3
Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:
x + 2 > 3
or
- (x + 2) > 3
Solving for x in the first inequality.
x > 1
Solving for x in the second inequality.
-x - 2 > 3
Adding 2 to both sides and multiplying by -1.
x < -5
So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.
Using interval notation.
(-∞, -5) U (1, ∞)
Thus,
The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.
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A=1/2h(a+b), solve for a
Step-by-step explanation:
2A=h(a+b)
2A=ha+hb
2A-hb=ha
2A-hb/h=a
A linear function contains the following points. What are the slope and y-intercept of this function?
Answer:
Your answer is b.
Step-by-step explanation:
for the slope, continue to add 2 to -4 until you reach 4
0 -4
1 -2
2 0
3 2
4 4
For y-intercept, when x=0, look at y. The y-intercept is -4
Hope this helps!
A stove heats food by adding _______ to the food.
F
G
H
J
If the diameter of a circle is 16 cm and the
intercepted arc length is 6m, what is the
measure of the central angle in radians?
3
8
3
7T
3
T
3²7
The measure of the central angle is 0.75 radians
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The length of an arc with an angle of Ф is given by:
Length of arc = (Ф/360) * (π * diameter)
The diameter is 16 cm and intercepted arc length is 6 cm, hence:
Length of arc = (Ф/360) * (π * diameter)
6 = (Ф/360) * (π * 16)
Ф = 42.97°
Ф = 42.97° * π/180 = 0.75 radian
The measure of the central angle is 0.75 radians
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an art gallery is selling replicas of some famous art work. a copy of the art work is dilated by a scale factor of 1/3 to create a replica of the original piece. if the area of some original artwork was 12 square feet what will be the area of the replica?
Answer:
4/3 square feet.
Step-by-step explanation:
To find the area of the replica, you need to use a formula that relates the area of the original figure and the area of the dilated figure by the scale factor1. The formula is:
Area of dilated figure = Area of original figure x (Scale factor)^2
In this case, the area of the original artwork is 12 square feet and the scale factor is 1/3. So, we plug these values into the formula and get:
Area of replica = 12 x (1/3)^2
Area of replica = 12 x 1/9
Area of replica = 4/3
So, the area of the replica is 4/3 square feet.
Hope this helps :)
what is factorise of 15
Answer:
The numbers that factorise 15 are: 1, 15, 3, 5
All these numbers divide 15 perfectly
Answer:
Factors of 15:
1, 3, 5, 15
Step-by-step explanation:
15/1 = 15
15/3 = 5
15/5 = 3
15/15 = 1
The factors are numbers 15 is divisible by that will give you a whole number.
If it is given that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S , then concluding that m ∠ J K L = m ∠ Q R S is an example of:
Concluding that m∠ J K L = m ∠ Q R S is an example of: substitution property of equality
What is Substitution Property of Equality?The substitution property of equality states that 'If a variable x is equal to another variable y, then x can be substituted in place of y in any equation/expression and y can be substituted in place of x in any equation/expression.
Now, we are told that m ∠ J K L = m ∠ X Y Z and m ∠ X Y Z = m ∠ Q R S.
Thus, concluding that m ∠ J K L = m ∠ Q R S is an example of: substitution property of equality
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A. 1) Given
2) Definition of midpoint
3) All right angles are congruent
4) HL theorem
2) Definition of a rectangle
3) Definition of a right triangle
4) HL theorem
2) Definition of midpoint
3) Definition of a right triangle
4) HL theorem
D. There is not enough information to prove the triangles congruent.
B. 1) Given
C. 1) Given
Reasons
GivenA midpoint splits a segment into two congruent partsA triangle with a right angle is a right triangleHL100 pts!!
Thanh rents a car. He has a fixed rate of $49.00 weekly, pays $14.00 per week for the optional insurance, and he spends $12.00 weekly on gas. What will Thanh's cost be per month (four weeks)?
Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.
To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.
Total weekly cost = Fixed rate + Insurance cost + Gas cost
Total weekly cost = $49.00 + $14.00 + $12.00
Total weekly cost = $75.00
The cost for Thanh per month (four weeks) = Total weekly cost × 4
Cost for Thanh per month (four weeks) = $75.00 × 4
Cost for Thanh per month (four weeks) = $300.00
Therefore, Thanh's cost per month (four weeks) will be $300.00.
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Graph the solution to the equations below. y = 1 4 x + 2 and y = −2x −7
f(x) = 2x - 7
g(x) = 3x² - 5x - 7
Find: f(g(x))
Express in standard form
The composite function of f(x) and g(x) is given as follows:
f(g(x)) = 6x² - 10x - 21.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The function g(x) in this problem is given as follows:
g(x) = 3x² - 5x - 7.
Hence, for the composite function in this problem, the lone instance of x in f(x) is replaced by 3x² - 5x - 7, as follows:
f(g(x)) = f(3x² - 5x - 7) = 2(3x² - 5x - 7) - 7 = 6x² - 10x - 21.
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3 over 5 =nothing over 20
ion even know yet
gyfujkl;kjbhvgfcdxsrtuiokl;, nbvghjkjhbgyu
x + 8 + 2x <= 2x + 13
Answer:
X = 15
Step-by-step explanation:
We move all terms to the left:
x+8+2x-(2x+13)=0
We add all the numbers together, and all the variables:
3x-(2x+13)+8=0
We get rid of parentheses:
3x-2x-13+8=0
We add all the numbers together, and all the variables:
x-5=0
We move all terms containing x to the left, all other terms to the right:
x=5
I cannot solve this question no matter how hard I try , I tried many different answers & kept getting 8.04 but it said it was wrong
hmm well, let's firstly convert all the mixed fractions to improper fractions, then we'll get the dot product.
\(\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > \hspace{5em}\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\)
\(\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{4\frac{2}{3}} \implies \cfrac{4\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{14}{3}} \\\\\\ \stackrel{mixed}{7\frac{1}{4}}\implies \cfrac{7\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{29}{4}}~\hfill \stackrel{mixed}{8\frac{1}{2}} \implies \cfrac{8\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill\)
\(\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > ~~\cdot~~\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{29}{4} \right)\left( \cfrac{7}{2} \right)~~ + ~~\left( -\cfrac{17}{2} \right)\left( \cfrac{14}{3} \right)\implies \cfrac{203}{8}-\cfrac{119}{3}\implies \cfrac{-343}{24} ~~ \approx ~~ \stackrel{ \textit{dot product} }{-14.29}\)
three is subtracted from a number that is doubled this entire result is tripled which equals twenty one what is the number
Answer: 5
Step-by-step explanation:
3(2x-3)=21
6x-9=21
6x=30
x=5
Please Help!!! I'll Give Best And Brainliest if it lets me!
Answer:
6
Step-by-step explanation:
this is the answer. have a great day.
What is the value of x in the figure shown below?
Answer:
30 degrees
Step-by-step explanation: