The following statement is true about the triangles (d) D = 77 and E = 79
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor,
Where the scale factor does not equal to one.
How to determine the true statements in the figure?From the attached image, we understand that there are two shapes
The shapes are triangles
One triangle is the scaled factor of the other
So, the triangles are similar shapes
As a general rule, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe corresponding angles of both figures are the sameUsing the above as a guide, we have the following
D =B = 77 -- by corresponding angles
Also, we have
E = A = 180 - 77 - 24 -- by corresponding angles
E = A = 79
Hence, the true statement is (d) D = 77 and E = 79
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Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of 300 gigabytes. (Recall that giga means billion.)
Answer: My new music player has a capacity of 3 * 10^11 bytes.
Step-by-step explanation: giga=billion=10^9. 300 in scientific notation is 3*10^2. Since 3 is between 1 and 10. So 10^2 * 10^9=10^11.
Seven times the sum of a number and 9
is 5
Seven times the sum of a number and 9 is 5 then the number is -58/7 .
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
We have been given that
Seven times the sum of a number and 9 is 5
Let the number is n.
let's write "the sum of a number and 9"
n + 9 .
Then, "seven times" the sum can be written as:
7 (n + 9)
This "is 5" or "is equal to 5" and can be written as:
7 (n + 9) = 5
To solve, first expand the term in parenthesis on the left side of the equation by multiplying each term in the parenthesis by
(7×n) + (7×9) = 5
7n + 63 = 5
Next, subtract 63 from each side of the equation to isolate the n term while keeping the equation balanced:
7n + 63 - 63 = 5 - 63
7n = -58
Now, divide each side of the equation by 7 to solve for n while keeping the equation balanced:
7n / 7 = -58 / 7
n = -58/7
The number is −58/7.
Hence , the number is -58/7 when a number is seven times its sum and 9 is 5.
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Which equation shows a slope of -5 and a y-intercept of (0,1)?
There are 7 new books and 8 used books on a shelf.
Only #15,17, and 19 please show work THANK YOU
The magnitude and direction of the vectors are
11. <0,4> :
Magnitude = 4
Direction = 90°
12. <-3,0>:
Magnitude = 3
Direction = 0°
13. <6,5>:
Magnitude = √(61)
Direction = 39.8°
14. <3,7>:
Magnitude = √58
Direction = 66.8°
15. <-2,1>:
Magnitude = √5
Direction = -26.57°
16. <-10,13>:
Magnitude = √(269)
Direction = -37.57°
17. <2,-5>:
Magnitude = √(29)
Direction = -68.2°
18. <8,-4>:
Magnitude = √(80)
Direction = -26.57°
19. <-4.-6>:
Magnitude = √(52)
Direction = 56.3°
20. <-1,9>:
Magnitude = √(82)
Direction = -83.66°
We are asked to find the magnitude and direction of the vectors given as <x, y>. We have the formulas for magnitude and direction of the vectors.
Magnitude = √(x²+y²)
and direction, θ = tan⁻¹(y/x)
11. The vector is <0,4>
Magnitude = √(0²+4²) = 4
Direction = tan⁻¹(4/0) = tan⁻¹∞ = 90°
12. The vector is <-3,0>.
Magnitude = √(-3²+0²) = 3
Direction = tan⁻¹(0/-3) = tan⁻¹0 = 0°
13.The vector is <6,5>
Magnitude = √(6²+5²) = √(61)
Direction = tan⁻¹(5/6) = 39.8°
14. The vector is <3,7>
Magnitude = √(3²+7²) = √58
Direction = tan⁻¹(7/3) = 66.8°
15.The vector is <-2,1>
Magnitude = √(-2²+1²) = √5
Direction = tan⁻¹(1/-2) = -26.57°
16.The vector is <-10,13>
Magnitude = √(13²+-10²) = √(269)
Direction = tan⁻¹(-10/13) = -37.57°
17.The vector is <2,-5>
Magnitude = √(2²+-5²) = √(29)
Direction = tan⁻¹(-5/2) = -68.2°
18.The vector is <8,-4>
Magnitude = √(8²+-4²) = √(80)
Direction = tan⁻¹(-4/8) = -26.57°
19.The vector is <-4.-6>
Magnitude = √(-4²+-6²) = √(52)
Direction = tan⁻¹(-6/-4) = 56.3°
20. The vector is <-1,9>
Magnitude = √(-1²+9²) = √(82)
Direction = tan⁻¹(9/-1) = -83.66°
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Grade 8 Pre-Algebra B
07.03
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected ove
the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?
Its A, A is congruent to B and B is congrument to c
The translation equation, often known as the vertical translation equation, is g(x) = f(x+k) + C.Because the triangles are not congruent, Figure B is not an exact replica of Figure A.
In what direction does a figure move on a coordinate grid?
An example of one of these is a translation. A geometric figure moves in the coordinate plane when it slides up, down, left, or right. The figure shifts its position but maintains its original orientation. Additionally, it maintains its size and shape.
The vertical translation equation, or the formula for translation, is g(x) = f(x+k) + C.
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Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. How many years was the loan period?
The loan that was borrowed by Georgina was for a period of 9 years.
How to calculate the value?From the information, Gregoria borrowed $2,450, to be paid back at 3.5% annual simple interest. She repays $3,221.75. The Interest will be:
= $3,221.75 - $2,450
= $771.75
Therefore, the time taken for the loan will be expressed as:
Interest = PRT/100
where P = Principal
R = Rate
T = Time.
Interest = PRT/100
771.75 = (2450 × 3.5 × T) /100
Cross multiply
8575T = 77175
Time = 77175 / 8575
Time = 9
The time is 9 years.
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In each figure, a is parallel to b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer. A line is reflected across line a, another line is reflected across line b to form a third line. a. Yes; it is one reflection after another with respect to the two parallel lines. b. No; it is a reflection followed by a translation. c. No; it is a reflection followed by a rotation. d. No; it is one reflection after another with respect to the two parallel lines. Please select the best answer from the choices provided A B C D
To determine whether the third figure is a translation image of the first figure, we say that; B: No; it is a reflection followed by a translation
How to Interpret Transformation of a figure?Transformation could be reflection, translation, rotation or even dilation.
Reflection can be thought of as the mirror image of a shape across a line.
Rotation is when one turns an object around a point
Translation is simply moving an object from one point to another without any change of dimension.
If we look at the given three figures in the attached image, we can see that the second image is the reflection or mirror image of the first figure.
After reflection, we can see that it is undergoes translation, which means it is moved apart from the first figure.
Thus, the third figure is a reflection of the first figure, and then it is translated.
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Mary earns $12 per hour, plus 10% commission on all her sales. Mary worked 10 hours and her sales were $1500. How much money did Mary earn?
5. CONSTRUCT ARGUMENTS Isabel wrote the expression 6 + 3 x 5 - 6+8+2 and asked Tamara to evaluate it. When Tamara evaluated it, she got a value of 19. Isabel told Tamara that her value was incorrect and said that the value should have been 38.
Who is correct? Justify your argument.
Answer:
none is correct
Step-by-step explanation:
6+3×5-6+8+2
6+15-6+8+2
6+9+10
=25
Here are two triangles.ABIs Triangle B a rotation of Triangle A? Explain your reasoning.HELP ASAPP
Answer
Triangle B is not a rotation of triangle A because on careful observation of this two triangles, one would see that they are mirror images of each other; reflections of each other.
A mental rotation of triangle A all through the 360° shows that at no point is it seeming exactly like triangle B.
This is why it is evident that triangle B is not a rotation of triangle A, rather, they are reflections of each other.
Hope this Helps!!!
How many ways can a three-person jury be selected from a pool of eleven people?
A three-person jury can be selected from a pool of eleven people in 165 ways.
What is meant by the term combination?A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the order of a selection is irrelevant. You can choose the items in any order in combinations. Permutations and combinations are often confused.We will employ the formula ⁿCₓ = n! / x! * (n - x)! to calculate combinations, where n is the total number of items and x represents the amount of items chosen at a time.For the given question;
The total number of person in the pool = 11.
The number of jury selected = 3.
Thus, the combination will be ⁿCₓ.
Where, n = 11 and x = 3.
¹¹C₃ = 11!/3!(11 - 3)!
Simplifying;
¹¹C₃ = 165
Thus, the number of ways in which three jury can be selected from 11 pool of members is 165.
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on a recent trip a trucker traveled 220 miles at a constant rate because of road conditions the trucker then reduce the speed by 25 mph an additional 30 miles traveled at a reduced rate the entire trip took five hours find the rate of the tracker for the first 220 miles
55 mph
if we assume it takes an hour for the last 30 miles then the rest of the time the trucker could go 55
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn’t think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
Answer to this question prove by induction
Answer:
solution: [tex]Sn= \frac{a_{1} (1-q^{n} )}{(1-q)} = \frac{1(1-4^{n}) }{1-4} = \frac{4^{n}-1 }{3}[/tex]
Step-by-step explanation:
This is a geometric series. Common ratio is 4.which example are polynomials select each correct answer
Step-by-step explanation:
The bottom two expressions are polynomials.
4 cups = ______ ounces
hint 1 cup = 8 ounces
Question 4 options:
2 oz
4 oz
12 oz
32 oz
Find the distance between (5, 10) and (8, 10)?
Answer:
3 units
Step-by-step explanation:
4x-3<-15 or 2x+4> 12
In given inequalities the value of x is x <-3 and x >4
What is inequalities ?Equations are not necessarily about having a "equal to" sign balanced evenly on both sides. It can occasionally refer to a "not equal to" connection, where one object is more than the other or less than. A connection that compares two numbers or other mathematical expressions in an unequal way is referred to as an inequality in mathematics. These mathematical statements are classified as inequalities in the algebraic language.
Given that :4x-3<-15 or 2x+4> 12
4x -3 <-15
4x < -12
x <-3
2x + 4 > 12
2x > 8
x >4
x <-3 and x >4
In given inequalities the value of x is x <-3 and x >4
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How do I solve this problem?
To solve this question we will compute the magnitude of each vector.
Recall that the magnitude of a vector
[tex]a\hat{i}+b\hat{j}[/tex]is:
[tex]\parallel a\hat{i}+b\hat{j}\parallel=\sqrt[]{a^2+b^2}.[/tex]Therefore, the speed of the first car is:
[tex]\parallel26\hat{i}+31\hat{j}\parallel=\sqrt[]{26^2+31^2}\text{.}[/tex]Simplifying the above equation we get:
[tex]\parallel26\hat{i}+31\hat{j}\parallel=\sqrt[]{676^{}+961}=\sqrt[]{1637}\approx40.46.[/tex]The speed of the second car is:
[tex]\parallel40\hat{i}\parallel=\parallel40\hat{i}+0\hat{j}\parallel=\sqrt[]{40^2+0^2}\text{.}[/tex]Simplifying the above equation we get:
[tex]\parallel40\hat{i}\parallel=\sqrt[]{40^2}=40\text{.}[/tex]Answer:
The first car is the faster car.
Speed= 40.46.
Find each missing measure
Answer:
<U = 54
<T = 72
Step-by-step explanation:
Find the angle measures
The marks on the sides means the sides are the same length
That means the base angles have the same measurement
<S = <U = 54
The sum of the angles of a triangle equals 180
<S + <U + < T = 180
54 + 54 + < T =180
108 + < T =180
<T =180-108
<T = 72
Answer:
m<U = 54°
m<T = 72°
Step-by-step explanation:
According to the isosceles triangle theorem ( If two sides of a triangle are equal , then the angles opposite to these sides are also equal. ),
ST = UT
So,
m<S = m<U.
Given that,
m<S = 54°
So,
m<U = 54°
Also, we know that the sum of the interior angles of a triangle is added up to 180 degrees.
So,
m<S + m<U + m<T = 180°
54° + 54° + m<T = 180°
108° + m<T = 180°
m<T = 180° - 108°
m<T = 72°
Yea thank I will need help
Solution
The diagram given is a right angle triangle
To find the value of x; we consider the relationship between the three sides.
Pythagoras theorem actually gave the relationship between the three sides of a right angle triangle.
By Pythagoras theorem;
[tex]\begin{gathered} x^2+8^2=13^2 \\ \\ \Rightarrow x^2=13^2-8^2 \\ \\ \Rightarrow x^2=169-64 \\ \\ \Rightarrow x^2=105 \\ \\ \Rightarrow x=\sqrt{105} \end{gathered}[/tex]x = 10.25
What is ab+ba?
and xz+zx
[tex]ab + ba[/tex]
Answers: 1) " 2ab ".
2) " 2xz ".
________________________
Step-by-step explanation:
ab + ba = ab + ab = 1ab + 1ab = (1+1)*ab = 2ab .
xz + zx = xz + xz = 1xz + 1xz = (1+1)*xz = 2xz.
________________________
A cell phone provider charges you
$35 a month for a phone plan and
charges $0.12 per MB of data used.
Write an equation in slope-intercept
form to represent the monthly price
as a function of the number of MB
used.
The equation, in slope-intercept form to represent the monthly price
as a function of the number of MB used is y = mx + c.
It is given in the question that the cell phone provider charges you
$35 a month for a phone plan and charges $0.12 per MB of data used.
Hence,
Total monthly charges = MB used*Charge per MB+ Fixed charge
Let y represents total monthly charges
x represents the charge per MB
m represents the MB used and,
c represents the fixed charge
Therefore, we can write the above equation as:-
y = mx + c
Hence the equation is written in the slope-intercept form.
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A factory produces zips. Testing shows that for
every 6000 zips tested, approximately 0.01
are defective. Estimate the number of
defective zips in a batch of 6000.
A) 60
B) 600
C) 0.01
D) 6
This is a probability question! Urgent help please!
Answer:
A) 60 that's i know !!!
Step-by-step explanation:
A) 60
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function
Based on the definition of the functions, the value of x if f(x) = g(x) is 3
How to determine the value of x?The equations of the functions are given as
f(x) = -2x + 4
g(x) = 2x - 8
It should be noted that the above equations are linear equations
From the question, we understand that the functions are equal
This means that, we have the following equation
f(x) = g(x)
Substitute the known values in the above equation
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms in the above equation
So, we have
2x + 2x = 8 + 4
Evaluate the like terms in the above equation
So, we have
4x = 12
Divide both sides by 4
x = 3
Hence, the value of x such that the equations are equal is 3
Graph the functionsSee attachment for the graph of the functions
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Eleanor owns a coffee shop.
She uses half a litre of mayonnaise each day.
Mayonnaise costs £2.45 for a 1 litre jar and £4.75 for a 2 litre jar.
Eleanor buys enough mayonnaise to last for 14 days.
What is the lowest price Eleanor can buy this mayonnaise for?
Show your working.
Mayonnaise cost of £4.75 for a 2 liter jar lowest price Eleanor can buy.
What is unitary method?This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
How to Apply the Unitary Method
Let's first list the data that we currently have. The number of ice creams is 5. It costs $125 for 5 ice creams.
step 1:Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.
Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.
Given:
Cots of 1 liter jar of Mayonnaise (I) = 2.45
Cost of 2 liter jar of Mayonnaise (II)=4.75
Cots of 1 liter jar of Mayonnaise (II)= 4.75/2= 2.375
If she eats half liter Mayonnaise in a day
So, she eat in 14 days = 0.5 x 14 = 7 liter
Hence, Mayonnaise cost of £4.75 for a 2 liter jar lowest price Eleanor can buy.
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The figure shows JN and KM intersecting at pointL.What value of x proves JK || MN ?
If JK || MN, then angle JKM is equal 61;
Also, angle JLK = 39 degrees as it is opposite angle to MLN.
Thus;
[tex]\begin{gathered} 3x+5+39+61=180\ldots\ldots\ldots\ldots\text{.sum of angles in triangle JLK} \\ 3x+105=180 \\ 3x=180-105 \\ 3x=75 \\ x=\frac{75}{3} \\ x=25 \end{gathered}[/tex]Thus x= 25 proves that JK || MN
Find the zeros of the polynomial 15x + 5.
Find the zeros of the polynomial 15x + 5.
Equating to 0:
[tex]15x+5=0[/tex]Subtracting 5:
[tex]15x=-5[/tex]Dividing by 15 and simplifying by 5:
[tex]\begin{gathered} x=\frac{-5}{15} \\ x=-\frac{1}{3} \end{gathered}[/tex]The graph of the derivative of a function f crosses the x-axis 3 times. What does this tell you about the graph of f ?
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
Well whenever any function crosses the x-axis, it means that the y-value is equal to zero.
In this case when the derivative passes the x-axis it indicates the tangent line corresponding to that x-value has a slope of zero, which when plotted is a horizontal line.
This means that the graph f has 3 horizontal tangent lines.
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
i got 100%