Given:
30-hour review course average a score of 620 on that exam.
70-hour review course average a score of 749.
To find:
The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.
Solution:
Let x be the number of hours of review course and y be the average score on that exam.
30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).
70-hour review course average a score of 749. So, the linear function passes through the point (70,749).
The linear function passes through the points (30,620) and (70,749). So, the linear equation is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]
Adding 620 on both sides, we get
[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]
We need to find the y-value for [tex]x=57[/tex].
[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]
[tex]y=183.825+523.25[/tex]
[tex]y=707.075[/tex]
[tex]y\approx 707.1[/tex]
Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.
Please help guys I’m really struggling
Answer: y = -4x - 4
Step-by-step explanation:
Point slope form: y - y1 = m(x - x1)
Plug in y1 and x1, and m. M is the slope, x1 and y1 are the values for a coordinate. You don't need to plug anything in for y or x, just y1 and x1.
First, find the slope. To find the slope, use this "formula" : [tex]slope=\frac{rise}{run} =\frac{y1-y2}{x2-x1}[/tex]
Find two coordinate points. Let's use (-2,4) and (0,-4). Based on this, we know that y1 is 4, y2 is -4, x1 is -2, and x2 is 0. Plug these into the formula:
[tex]\frac{4--4}{-2-0} =\frac{4+4}{-2} =\frac{8}{-2}=-4[/tex]
Then, pick any point to plug into the equation. Let's use (0,-4)
Finally, plug everything into the equation:
y - - 4 = -4(x - 0)
y + 4 = -4x
y = -4x - 4
Answer:
[tex]y - 4 = - 4(x + 2)[/tex]
Step-by-step explanation:
Point Slope Form is a algebraic formula when we know a pair of points and it
slope.
It can be represented by
[tex]y - y_{1} = m(x + x _{1})[/tex]
where m is the slope and x 1 and y 1 are the points we know.
The coordinates we know are (-2,4) so we just plug it in.
We also know the slope of the line is rise/run. Look at point (-2,4). The next consecutive point before that is x intercept (-1,0). Let use the slope formula to find the slope
[tex] \frac{0 - 4}{ - 1 - ( - 2)} = \frac{ - 4}{1} = - 4[/tex]
So the slope or m is -4. Plug this in and the coordinates into point slope formula.
[tex]y - 4 = - 4(x - ( - 2)[/tex]
[tex]y - 4 = - 4(x + 2)[/tex]
That the answer.
What is the value of x?
1/2(x+6)=18
Answer:
30
Step-by-step explanation:
Multiply by 2 to 18, x+6=36
subtract 6 x=30
x=30
HELP ASAP 10 POINTS AND BRAINLIEST
Answer:
135
Step-by-step explanation:
The area is given by
A = bh where b is the base and h is the height
A = 9* 15
A =135
Answer:
[tex]135 \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]area = b \times h \\ = 9 \times 15 \\ = 135 \: {units}^{2} [/tex]
help with this question please
Show all work to multiply (3+ Square root of -16)(6- square root of -64)
Answer:
1042-96i
Step-by-step explanation:
(3 + 16i)(6 - 64i)
6(3 + 16i)(3 - 32i)
(6) 9 - 96i + 48i +1024
99 boys and 1 girl are in a lecture theatre. how many boys must leave the theatre so that the percentage of boys becomes 98%?
99 boys and 1 girl makes 99 percent of boys. To make it 98%, 50 boys must leave the theatre, so there are 49 boys and 1 girl, making 98% of boys.
help pls and explain!!!
If x^2 + kx + 6 = (x+n)(x + 3) for all values of x, where k and n are constants, what is the value of k?
A) 5
B) 3
C) 2
D) 1
Answer:
A) 5
Step-by-step explanation:
We are given that:
[tex]x^2+kx+6=(x+n)(x+3)[/tex]
Where k and n are constants.
And we want to find the value of k.
We can expand the right-hand side:
[tex]\displaystyle =x(x+n)+3(x+n)\\ \\ = x^2+nx+3x+3n \\ \\ = x^2 + (n+3)x+3n[/tex]
Hence:
[tex]x^2+kx+6=x^2+(n+3)x+3n[/tex]
The coefficients of each term must be equivalent. In other words:
[tex]k=n+3\text{ and } 6=3n[/tex]
Solve for n:
[tex]n=2[/tex]
Now, we can solve for k:
[tex]k=(2)+3=5[/tex]
Our answer is A.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 63.9
Step-by-step explanation:
We have:
[tex]\frac{QR}{sin35}[/tex] = [tex]\frac{78}{sin90}[/tex]
=> QR × sin90 = 78 × sin35
=> QR × sin90 = 44.7
=> QR = 44.7
But, we also have: [tex]x^{2}[/tex] + [tex]QR^{2}[/tex] = [tex]78^{2}[/tex] <=> [tex]x^{2}[/tex] + [tex]44.7^{2}[/tex] = [tex]78^{2}[/tex] <=> [tex]x^{2}[/tex] = 6084 - 1998.09
=> [tex]x^{2}[/tex] = 4085.91
=> x = [tex]\sqrt{4085.91}[/tex] = 63.9211.. = 63.9
<3 Have a nice day!!
pplied for a job as a cashier at a hardware store. As part of her employment screening, she was asked to take an exam that had general mathematical aptitude questions in it. This type of selection test is referred to as a
Answer:
cognitive ability
Step-by-step explanation:
Now, if you solve for x, what is the result?
Answer:
x = 3/9
= 1/3
Step-by-step explanation:
i did this assignment and got it right
use the order of operations -5 + 3(7.2 - 3.2)
Answer:
-5 + 3(7.2 - 3.2) equals 7.
Step-by-step explanation:
The order of operations states the order in which different mathematical operations should be done first, you can use the mnemonic PEMDAS to remember the order to complete each operation. PEMDAS states that the order must be followed as Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. In the expression -5 + 3(7.2 - 3.2), the three mathematical operations being used are subtraction, multiplication, and parenthesis, so based on PEMDAS, the order to complete them is parenthesis, multiplication, and subtraction. -5 + 3(7.2 - 3.2) = -5 + 3(4) = -5 + 12 = 7, so that is your final answer.
[tex]\displaystyle\bf -5+3(7.2-3.2)=7\\\\1)\:7.2-3.2=4\\\\2)\:4\cdot3=12\\\\3)\:12-5=7[/tex]
translate the sentence into an equation
three more than the quotient of a number and 2 is 9
Answer:
Well the correct answer is 9=2+(x/3) or
(3/x)+2=9
In general, what can you say about the difference when you subtract a larger integer from a smaller integer?
Answer:
To subtract integers, change the sign on the integer that is to be subtracted. If both signs are positive, the answer will be positive. If both signs are negative, the answer will be negative. If the signs are different subtract the smaller absolute value from the larger absolute value
help pls and explain!!
Each molecule of aluminum oxide (Al2,03) is
composed of 2 aluminum atoms and 3 oxygen atoms.
How many more oxygen atoms than aluminum
atoms are present in 100 molecules of aluminum
oxide?
Answer:
100
Step-by-step explanation:
[tex](100 \times 3) - (100 \times 2) = 100 [/tex]
A teacher asks students to determine the accuracy of this statement.
A reflection over the x-axis and then over the y-axis results in the same transformation as a 180degree rotation about the origin of the original figure.
Kwame’s explanation of the accuracy of the statement is shown below.
Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3).
Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).
Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).
Step 4: Rotate the pre-image 180degree: (–1, –2), (–1, –4), (–2, –3).
Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.
Which best explains Kwame’s solution?
Kwame’s explanation and solution are incorrect. He reflected the image over the y-axis in step 2 and the x-axis in step 3, instead of the reverse.
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Kwame’s explanation and solution are incorrect. When reflecting over the x- and y-axes, he negated the incorrect coordinate in the ordered pair.
Kwame’s explanation and solution are incorrect. The coordinates of the rotated figure should be switched and negated, not just negated.
Answer:
B. Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Step-by-step explanation:
I just did it, and thankfully, all was well! :) :) :)
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation. Rotation, translation and reflection produce congruent images.
The vertices of the pre-image is (1, 2), (1, 4), (2, 3). It is reflected over the x axis to get (1, –2), (1, –4), (2, –3)It is then reflected over the y axis to get (-1, 2), (-1, 4), (-2, 3) instead of (-1, –2), (-1, –4), (-2, –3).Rotating the vertices 180 degrees gives (-1, –2), (-1, –4), (-2, –3).
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Find out more on transformation at: https://brainly.com/question/1620969
What is the length of the unknown leg in the right triangle…?
As we know,
In a triangle, the sum of lengths of two side is greater than the third side.
[tex]20 + 25 > b[/tex]
[tex]b + 20 > 25[/tex]
[tex]25 + b > 20[/tex]
Answer = 15m
Completing the Square
Guided Practice
Solve the equation by completing the square. If necessary, round to the nearest hundredth.
2x2 - 10x - 20 = 8
A. 27 - 27
B. 7
C.7, -2
Answer:
C.7, -2
Step-by-step explanation:
A quadratic equation is a polynomial of degree two. A quadratic equation is in the form:
ax² + bx + c = 0; where a, b, c are constants.
Quadratic equation can be solved using different methods, such as completing the square method, quadratic formula.
Solving the equation 2x² - 10x - 20 = 8 using completing the square:
2x² - 10x - 20 = 8
2x² - 10x = 28
Divide through by 2, to make the coefficient of x² to be 1:
x² - 5x = 14
Add to both sides, the square of half of the coefficient of x [i.e. (-5/2)² = 6.25]
x² - 5x + 6.25 = 14 + 6.25
(x - 2.5)² = 20.25
taking square root of both sides:
x - 2.5 = √20.25
x - 2.5 = ±4.5
x = 2.5 ± 4.5
x = 2.5 + 4.5; or x = 2.5 - 4.5
x = 7 or x = -2
The z- score for a mark of 56 in a test with a mean of 60 and standard deviation of 8 is
Answer:
z = - .5
Step-by-step explanation:
z = (x - μ)/ σ
z = 56 - 60/8 = -.5
Help please I don’t understand
Answer:
you need to solve for 'X'
mean 49 = 55 + 42 + 32 +48 + 55 + X
49 = (232+X) / 6
49 * 6 = 232 + X
294 = 232 + X
294 - 232 = X
62 = X
so therefore X is 62
Step-by-step explanation:
please give me a brainliest
Which arc is a minor arc?
A)SQ
B)PSR
C)PS
D)SO
Answer:
Answer: The arc PS would be a minor arc · Step-by-step explanation: As a minor arc is one that is less that 180 degrees, it would be the only viable ...
Divisor mayor común de 28 y 48
Answer:
mcd(28,48) = 4
Para encontrar el mcd de 28 y 48:
Los factores de 28 son 28, 14, 7, 4, 2, 1.
Los factores de 48 son 48, 24, 16, 12, 8, 6, 4, 3, 2, 1.
Los factores en común de 28 y 48 son 4, 2, 1, los cuales intersectan los dos conjuntos arriba.
En la intersección de los factores de 28 ∩ factores de 48 el elemento mayor es 4.
Por lo tanto, el máximo común divisor de 28 y 48 es 4.
En la granja hay que vacunar a 525 terneros si llevaron vacunados 102 ¿ cuantos faltan por vacunar ?
Respuesta:
423
Explicación paso a paso:
En la finca hay que vacunar 525 terneros, si se vacunaron 102, ¿cuántos quedan por vacunar?
Dado :
Número de terneros que deben ser vacunados = 525
Número de terneros que han sido vacunados = 102
Número de terneros que quedan por vacunar = (Número de terneros que deben ser vacunados - Número de terneros que han sido vacunados)
Número de terneros que quedan por vacunar = (525 - 102) = 423
Is it possible to relate cyclones to mathematics? If yes, explain your thinking with the help of drawings (no need to use downloaded images) What are the mathematical concepts, theorems and shapes related to cyclones.
Answer:
hi shaurya
Step-by-step explanation:
mila first stands on a diving board is 3 feet above surface of the water .she then dives to the bottom of the pool to a depth of 10 feet
Answer:
She Dives 13 Feet
Step-by-step explanation:
3+10=13
Mila's depth from the diving board to the bottom of the pool is 13 feet.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Mila first stands on a diving board 3 feet above the surface of the water .she then dives to the bottom of the pool to a depth of 10 feet.
The total depth will be calculated as below:-
Depth = 3 + 10
Depth = 13 feet
Therefore, Mila's depth from the diving board to the bottom of the pool is 13 feet.
To know more about expression follow
https://brainly.com/question/878985
#SPJ2
plz help me find the answers
Answer:
Correct answer B 130
Step-by-step explanation:
<FAE=90
<AFE=40
We have a triangle, so <FEA= 180-90+40=50
<FEA+FEB= 18-, so 180-50=130
AB parralel to CD then <ECD=130
D=rt What does T equal? Lol how is this possible
Answer:
t = D/r
Step-by-step explanation:
you rearrange the equation so that is the subject. when you bring something over the equal sign, it reverses the function so D = r×t becomes t = D/r
solve x in the diagram below
Answer:
60
Step-by-step explanation:
180-100 = 80
80-20 = 60
The following figures are not drawn to scale but AB and CD are straight lines. Find x.
Answer:
x=60
Step-by-step explanation:
solve, 180-(90+x) = 180-(30+2x)
Type the correct answer in each box. Use numerals instead of words
Answer:
a) 1.73
b)1.32
Step-by-step explanation:
y = f(x) = 3^x
f(1/2) = 3^1/2 = √(3) = 1.73
f(1/4) = 3^1/4 = 1/4√3 = 1.32
Solve the following system of equations algebraically.
y=2x-12
y=x+22+3
Answer:
x=37
Step-by-step explanation:
because
y=y
or as, 2x-12=x+22+3
or as, 2x-x=12+22+3
or as, x = 37