Answer:
The constant of variation is $1.50
Step-by-step explanation:
Given
Point 1 (1,2)
Point 2 (5,8)
Required
Constant of Variation
Though the graph would have assisted in answering the question; its unavailability doesn't mean the question cannot be solved.
Having said that,
the constant variation can be solved by calculating the gradient of the graph;
The gradient is often represented by m and is calculated as thus
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1, y_1) = (1,2)\\(x_2, y_2) = (5,8)[/tex]
By substituting values for x1,x2,y1 and y2; the gradient becomes
[tex]m = \frac{8 - 2}{5 - 1}[/tex]
[tex]m = \frac{6}{4}[/tex]
[tex]m = \frac{3}{2}[/tex]
[tex]m = 1.50[/tex]
Hence, the constant of variation is $1.50
Answer:
A
Step-by-step explanation:
In Mrs. Nathan's class, there are 16 boys and 20 girls. What is the ratio of girls to boys in Mrs. Nathan's class?
Answer:
5:4
Step-by-step explanation:
In Mrs. Nathan's class, the ratio of girls to boys is 5:4.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, In Mrs. Nathan's class, there are 16 boys and 20 girls.
the ratio of girls to boys = 20/16
the ratio of girls to boys = 5/4
Therefore, the ratio of girls to boys in Mrs. Nathan's class is 5: 4.
Learn more about ratios here:
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I am thinking of a number. It is less than 500. It’s cube root is an integer. What is the largest possible value of this number
Answer:
[tex]343[/tex]
Step-by-step explanation:
[tex]1^{3} =1\\2^{3} =8\\3^{3} =27\\4^{3} =64\\5^{3} =125\\6^{3} =216\\7^{3} =343\\8^{3} =512[/tex]
[tex]\sqrt[3]{x } >500[/tex]
[tex]\sqrt[3]{343} >500[/tex]
Solve the inequality 8(x + 1) > 7(x + 2)
Answer:
7(2 - x)
Step-by-step explanation:
Answer:
x>6
Step-by-step explanation:
8(×+1)>7(x+2)
(8×x)+(8×1)>(7×x)+(7×2)
8x+8>7x+14
Now subtract 8 and 7x from each side of the inequality to solve for x while keeping the inequality balanced:
-7x+8x+8-8 > -7x+7x+14-8
(-7+8)x+0>0+6
1x>6
x>6
Need Math help ASAP
Answer:
35 seconds
Step-by-step explanation:
At negative values he is inside the volcano, when he reaches 0 he will be at the top of the volcano
At 35 seconds, the elevation is 0, so he is at the top of the volcano
product 48 and sum 14 what are the factors
Answer:
Step-by-step explanation:
Let's write a system.
Let's say that the variables are x and y.
xy=48
x+y=14
Solve for one of the variables, let's say, x.
x=14-y.
Now substitute x into the 1st equation.
(14-y)y=48
Simplify.
-y²+14y=48
Make it into a quadratic equation.
-y²+14y-48=0
Make sure y²'s coefficient is one. Divide everything by -1
y²-14y+48=0
Now factor!
What factors add up to 14 and multiply to 48.
6 and 8!
Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.
y²-6y-8y+48=0
Group.
(y²-6y)+(-8y+48)=0
y(y-6)-8(y-6)=0
(y-8)(y-6)=0
y-8=0
y-6=0
y=8 y=6
now let's substitute each y value into y²-14y+48=0
8²-14(8)+48=0
64-112+48=0
0=0. so y=8 checks out!
6²-14(6)+48=0
36-84+48=0
0=0 so y=6 also checks out!
Choose one y value and solve for x, in each equation :
xy=48
x+y=14
8x=48
x+8=14
x=6
x=6
It checks out!
so the factors are
x=6 y=8.
Mapiya writes a series of novels. She earned \$75{,}000$75,000dollar sign, 75, comma, 000 for the first book, and her cumulative earnings double with each sequel that she writes.
Answer:
[tex]E(n)=75000 \times 2^n[/tex]
Complete question:
write a function that gives mapiyas cumulative earnings E(n), in dollars when she has written n sequel's
Step-by-step explanation:
According to the question, she earned $75000 for the first book.
Also,We are given that her cumulative earnings double with each sequel that she writes.
Assuming she has written n sequel's
Now since we are given that her cumulative earnings double with each sequel
So, her initial earning will be [tex]2^n[/tex] times
So, her earning will be : [tex]75000 \times 2^n[/tex]
Now we are given that cumulative earnings is denoted by E(n)
So, the function becomes :[tex]E(n)=75000 \times 2^n[/tex]
Hence a function that gives Mapiya's cumulative earnings E(n), in dollars when she has written n sequel's is [tex]E(n)=75000 \times 2^n[/tex]
can some one help me this please
What is the sum of this arithmetic series?
Answer:
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Step-by-step explanation:
Explanation
Let a , a+d , a+2 d , ..........a+(n-1)d +....... is an arithmetic sequence
The sum of the sequence is called arithmetic series
The [tex]n^{th}[/tex] term of the sequence
[tex]t_{n} = a + (n-1) d[/tex]
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Here 'a' is the first term of the sequence
and 'd' be the difference between two values
sum of first term
put n=1 ⇒ [tex]S_{1} = a[/tex]
Put n =2 ⇒ [tex]S_{2} = \frac{2}{2} (2 a + (2-1)d)[/tex]
[tex]S_{2} = 2 a + d[/tex]
......and so on
The sum of the arithmetic series
[tex]S_{n} = \frac{n}{2} (2 a + (n-1) d)[/tex]
Write this equation in slope-intercept form. 5x - 6y = -6 *
Answer:
y = 5/6x +1
Step-by-step explanation:
5x - 6y = -6
We want the equation in the form
y = mx+b where m is the slope and b is the y intercept
Subtract 5x from each side
5x -5x - 6y =-5x -6
-6y = -5x -6
Divide each side -6
-6y/-6 = -5x/-6 -6/-6
y = 5/6x +1
What angle corresponds to ∠M?
Answer:
iuhi on edge its c
Step-by-step explanation:
Any one can help me please please I need help please each one 3 step explanation
Answer:
a) Area of wall to be painted = 114 sq ft
b) Number of cans required = 2×5 = 10
c) Total cost of paint = $338.43
Step-by-step explanation:
Part a)We are asked to find the area of wall that needs to be painted.
we need to subtract the area of window from the area of wall.
We know that area of a rectangular shape is given by
Area = Width×Length
Area of whole wall = 8×15 = 120 sq ft
Area of window = 2×3 = 6 sq ft
Area of wall to be painted = 120 - 6 = 114 sq ft
Part b)1 can of paint will cover 25 sq ft of area.
So to cover the area of wall to be painted,
114/25 = 4.56
since number of cans cannot be in fraction so we would need 5 cans
Since two coats of paints are needed so
Number of cans required = 2×5 = 10
Part c)1 can of paint costs $29.95
We have total 10 cans
$29.95×10 = $299.5
There is also a 13% tax so the total cost is
$299.5×0.13 = $38.93
Total cost of paint = $299.5 + $38.93
Total cost of paint = $338.43
Solve for j.
-2j + 39 = 111
j=
Answer:
reeeeeerre
Step-by-step explanation:
Answer:
-2j+39=111=
-2j+39=111-39
-2j=72
-2j÷2=72÷2=
j=36
the answer is j=36
Simplify, using the distributive property and then combining like terms.
5(3a+b)−2(3a+b)
Answer:
9a + 3b
Step-by-step explanation:
Given
5(3a + b) - 2(3a + b) ← distribute both parenthesis
= 15a + 5b - 6a - 2b ← collect like terms
= 9a + 3b
Answer:
The final answer would be [tex]9a + 3b[/tex] .
Step-by-step explanation:
Solve the following equation:
[tex]5(3a+b)-2(3a+b)[/tex]
Use Distributive Property:
[tex]5(3a+b)-2(3a+b)[/tex]
[tex]15a + 5b - 6a - 2b[/tex]
-Combine [tex]15a[/tex] and [tex]6a[/tex]:
[tex]15a + 5b - 6a - 2b[/tex]
[tex]9a + 5b - 2b[/tex]
-Combine [tex]5b[/tex] and [tex]-2b[/tex]:
[tex]9a + 5b - 2b[/tex]
[tex]9a + 3b[/tex]
So, the answer is [tex]9a + 3b[/tex] .
in this figure what is m 5?
Answer:
m<5 = 95 degrees
Step-by-step explanation:
Let's first find m<1
=> m<1 = 180-85
=> m<1 = 95 degrees
Since,
m<1 = m<5 (Corresponding angles)
So,
m<5 = 95 degrees
find the area of the shape
37.68 is the area of the Pac-Man
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept and what is the y-intercept of the line?
Answer:
Equation to be used: Point- Slope form [tex] y-y_1= m(x-x_1)[/tex]
y-intercept = - 12
Step-by-step explanation:
He should use point - slope form equation.
It is given that, line is passing through the points[tex] (1,\: -8) = (x_1\:y_1)[/tex] and has a slope m = 4.
The equation of line in point-slope form is given as:
[tex]y-y_1= m(x-x_1)\\y-(-8) = 4(x-1)\\y+8 = 4x - 4\\y = 4x - 4 -8\\\huge\red{\boxed{y= 4x - 12}}...(1)\\Equating\: equation\: (1) \: with;\\y = mx + b \\y-intercept\: (b) = -12[/tex]
Answer:
The answers are B and D.
Step-by-step explanation:
What is the highest common factor of 50 and 90?
Answer: The gcf is 10
Step-by-step explanation:
find the second term of this sequence? 3n^2-1
Answer:
11.
Step-by-step explanation:
Because you wanted to find the second term, just substutite n=2 into the formula.
Thus, 3(2)^2 - 1 = 3(4) - 1 = 11
Answer:
11Step-by-step explanation:
We get the second term by just plug in 2 (instead of n) in the sequence formula:
second term = 3×(2)² - 1 = 11
The store's rectangular floor is 42 meters long and 39 M wide how many square meters of flooring do they need use estimation access to the reasonableness of your answer
Answer: They need to use 1,638 square meters of flooring.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given, and apply the next formula:
Area of a rectangle: length x width
Replacing with the values given and solving for the area (A):
A = 42 x 39 = 1,638 m2
They need to use 1,638 square meters of flooring.
Feel free to ask for more if needed or if you did not understand something.
A function g(x) is defined as shown.
g(x) =
2 + 3x,
0.5x + 10, 4 < x < 8.
16
What is the value of g(4)?
Answer:
4
Step-by-step explanation:
I love your name. my friend is also named like that. and she has a twin that is named jessicamarie.......oof!
OA ⊥ OC start overline, O, A, end overline, \perp, start overline, O, C, end overline \qquad m \angle BOC = 6x - 6^\circm∠BOC=6x−6 ∘ m, angle, B, O, C, equals, 6, x, minus, 6, degrees \qquad m \angle AOB = 5x + 8^\circm∠AOB=5x+8 ∘ m, angle, A, O, B, equals, 5, x, plus, 8, degrees Find m\angle BOCm∠BOCm, angle, B, O, C:
Answer:
42 degrees.
Step-by-step explanation:
[tex]\angle BOC+\angle AOB=90^\circ $(Complementary Angles)\\6x - 6^\circ+5x + 8^\circ=90^\circ\\6x+5x-6^\circ+ 8^\circ=90^\circ\\11x+ 2^\circ=90^\circ\\11x=90^\circ-2^\circ\\11x=88^\circ\\$Divide both sides by 11\\x=8^\circ\\$Therefore:\\m\angle BOC=6x - 6^\circ\\=6(8) - 6^\circ\\=48-6\\=42^\circ[/tex]
The measure of angle BOC is 42 degrees.
Answer:
BOC = 42º
Step-by-step explanation:
Angle BOC is equal to 42 degrees, due to these steps -
1. Create the equation which will result to be -
6x - 6 + 5x + 8 = 90
2. Simplify by adding variables and numbers together -
11x + 2 = 90
3. Subtract 2 from both sides to get -
11x = 88
4. Divide by 11 on both sides to get-
x = 8
5. Substitute x in angle BOC as 8 to get this equation -
6(8) - 6
6. Solve
48 - 6 =
42º
Your final answer for angle BOC is 42º!
I need help ASAP please help me I’ll give brainliest
Answer:
Volume = 1,017.4m^3 .
Step-by-step explanation:
[tex]V = \frac{1}{3} pir^{2}h \\h (height) = 12m\\r (radius ) = 9m\\PI = 3.14\\V =\frac{1}{3} * 3.14 *9^{2} *12\\\\V = 1,017.36\\V = 1,017.4m^{3} .[/tex]
Please help with this question!!!
In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and -2 for every incorrect answer and 0 for not supplying any answer. If Yash scored 94 marks in a test, what are the possibilities of his marking correct or wrong answer
Answer:
1. 47 correct, 0 wrong and 3 unanswered
2. 48 correct, 1 wrong and 1 unanswered
Step-by-step explanation:
Given;
Total number of questions = 50
For correct answers = 2
For wrong answers = -2
Unanswered questions = 0
Yash scored 94 marks
Let c, w and u represent the number of correct, wrong and unanswered questions
2×c - 2 × w + 0×u = 94
2c -2w = 94 .....1
And;
c + w + u = 50 .....2
We have 2 equations and 3 unknowns
By observing the problem, we can see two possible solutions;
Case 1: Assuming he did not miss (get wrong) any answer;
He needs to score 47 answers right;
47 × 2 = 94
Then;
c = 47 w = 0 and u = 50 - (47+0) = 3
47 correct, 0 wrong and 3 unanswered
Case 2: Assuming he got one answer wrong;
He would need to score one more answer right compared to the first case;
(47+1) × 2 - 1 × 2 = 96 - 2 = 94
c = 47+1 = 48
w = 1
u = 50 - (48+1) = 1
So he need to score 48 correct answers, 1 wrong answer and 1 unanswered.
BEG is a triangle.
ABC and DEF are parallel lines.
Work out the size of angle x.
the weights, in pounds, of the upper class men offensive line players for a college are shown below:
322, 290, 321, 326, 330, 315, 311, 292, 290
What is the average, or mean, weight of the upper-class men offensive players? provide your answer with 3 sig figs.
1) 311 pounds
2) 315 pounds
3) 290 pounds
4) 318 pounds
Answer:
311 pounds
Step-by-step explanation:
Here, we are to calculate the average weight of the upper-class men offensive players
To calculate this, we need to sum up all the weights and divide by their count
Mathematically, that would be;
Average weight = (322+290+321+326+330+315+311+292+290)/9 = 2,797/9 = 310.77778
Now this written in 3 significant figures would be 311 pounds
Answer:
311
Step-by-step explanation:
You add all of the numbers first (2797)
Then you divide by how many numbers there were (9)
You get 310.7778
Then you round with 3 sig figs.
That is 311
Hope this helps:D
Ratio of three angles of a triangle is 1 : 2 : 3. Find the angles.
Answer:
30⁰ , 60⁰ , 90⁰
Step-by-step explanation:
Let the angles x , 2x , 3x
By angle sum property:
x + 2x + 3x = 180⁰
6x = 180⁰
x = 30⁰
Angles are : 30⁰ , 60⁰ , 90⁰
Answer:
30°, 60°, 90°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the parts of the ratio, 1 + 2 + 3 = 6 parts
Divide to find the value of one part of the ratio
180° ÷ 6 = 30° ← value of 1 part of the ratio, thus
2 parts = 2 × 30° = 60°
3 parts = 3 × 30° = 90°
Thus angles are 30°, 60° and 90°
Find the distance between points (5,1) and (3,4) to the nearest tenth
Answer:
3.6 units (nearest tenth)
Step-by-step explanation:
distance formula
= [tex] \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
Thus, distance between the 2 points
= √[(5 - 3)² + (1 - 4)²]
= √[ 2²+ ( - 3)²]
= √13
= 3.6 units (nearest tenth)
Which linear equation represents a line with a slope of 9/4 and a y-intercept of 0? plz help giving out brainliest
Answer:
y = 9/4x.
Step-by-step explanation:
According to slope-intercept form, y = mx + b where m is the slope and b is the y-intercept.
So, y = 9/4x + 0
y = 9/4x.
Hope this helps!
The required equation of the line is given as 9/4x with a slope of 9/4 and a y-intercept of 0.
Given that,
The linear equation represents a line with a slope of 9/4 and a y-intercept of 0 is to be determined.
What is the slope of the line?
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
Standard equation of the line,
y = mx + c
Put , = 9/4 and c = 0
y = 9/4x + 0
y = 9/4x
Thus, the required equation of the line is given as 9/4x.
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Solve for x -2x + 5<7
a)x>-1
b)xc-1
c)x>-6
d)x<-6
Answer:
x>−2
Step-by-step explanation:
Let's solve your inequality step-by-step.
x−2x+5<7
Step 1: Simplify both sides of the inequality.
−x+5<7
Step 2: Subtract 5 from both sides.
−x+5−5<7−5
−x<2
Step 3: Divide both sides by -1.
−x
−1
<
2
−1
x>−2
Answer:
x>−2
