Answer:
[tex]Y = 441[/tex]
Step-by-step explanation:
Given
M = 27 when Y = 16 and X = 9
Required
Find Y when M = 7 and X = 2
We start by getting the algebraic representation of the given statement
[tex]X^2 \alpha \frac{1}{\sqrt Y} \alpha M[/tex]
Convert the variation to an equation; we have
[tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Where K is the constant of variation;
When M = 27; Y = 16; X = 9, the expression becomes
[tex]9^2 = \frac{K * 27}{\sqrt{16}}[/tex]
This gives
[tex]81 = \frac{k * 27}{4}[/tex]
Make K the subject of formula
[tex]K = \frac{81* 4}{27}[/tex]
[tex]K = \frac{324}{27}[/tex]
[tex]K = 12[/tex]
Solving for Y when M = 7 and X = 2
Recall that [tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Substitute values for K, M and X
[tex]2^2 = \frac{12 * 7}{\sqrt{Y}}[/tex]
[tex]4 = \frac{84}{\sqrt{Y}}[/tex]
Take square of both sides
[tex]4^2 = (\frac{84}{\sqrt{Y}})^2[/tex]
[tex]16 = \frac{7056}{Y}[/tex]
Make Y the subject of formula
[tex]Y = \frac{7056}{16}[/tex]
[tex]Y = 441[/tex]
The base of 14-foot ladder is 6 feet from a building. If the ladder reaches the flat roof, how tall is the building?
Answer:
Approximatly 12.65
Step-by-step explanation:
You would use the pythagorean Theoram for this.
[tex]a^{2}+6^{2}=14^{2}[/tex]
[tex]a^{2}+36=196[/tex]
Subtract 36 from both sides:
[tex]a^{2}=160[/tex]
Square 160 to remove the exponent on "a":
[tex]a=\sqrt{160}[/tex]
[tex]a≈ 12.65[/tex]
If the ladder reaches the flat roof, then the height of the building will be 12.65 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The base of 14 feet ladder is 6 feet from a building. Then the length of the hypotenuse is 14 feet and the base is 6 feet. Then the height of the building will be given by the Pythagoras theorem.
If the ladder reaches the flat roof, then the height of the building will be
H² = P² + B²
14² = P² + 6²
196 = P² + 36
P² = 196 - 36
P² = 160
P = 12.65 feet
If the ladder reaches the flat roof, then the height of the building will be 12.65 feet.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ2
Find the approximate side length of a square game board with an area of 155in2.
The side of a square is the square root of the area.
Side = sqrt(155)
Side = 12.45 inches. (Round answer as needed)
The sum of two numbers is 190. The sum of their digits is 10.
Which pair of points has a slope of 4? Question 4 options: (0, 4), (4, 0) (3, 0), (–1, –1) (1, 4), (–1, 4) (0, –3), (1, 1)
Answer:
(0,-3) and (1,1)
Step-by-step explanation:
In order to have a slope of 4, the y coordinates need to differ by 4, and the x coordinates by 1. This is because slope is equal to rise/run. Rise being difference in y value and run difference in x.
In this pair of coordinates, the y coordinates differ in +4 (-3 and 1) and the x coordinate differs by 1 (0 and 1).
Therefore this is the pair of points with a slope of 4.
Hope this helped!
The pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)
The formula for calculating the slope of a line passing through two points is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We need to get which of the coordinates will result in a slope of 4.
Using the coordinate points (0, –3), (1, 1)
[tex]m=\frac{1-(-3)}{1-0}\\m=\frac{1+3}{1}\\m=\frac{4}{1}\\m=4[/tex]
Hence the pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)
Learn mroe here: https://brainly.com/question/23935638
Select the appropriate response.
An isosceles triangle has vertices at (1,1) and (3, 3). Which of the following could be
the coordinates of the third vertex?
A. (2.1)
B. (3.2)
C. (4,1)
D. (5,1)
Choose
Answer:
D. (5,1)
Step-by-step explanation:
Because it is an isosceles triangle, the next point we choose must result in two sides with the same length. This means that either the two new sides are equal, or that one of the new sides is equal to the original side. If we wanted both of the new sides to be equal, they would have to be equal distance from the new point and one of the points of the original line. However, none of the options result in both new lines being the same length.
(2,1) would result in one new length being 1 unit long (2-1 x-coordinates) and the other being square root 5 (distance from point 2,1 to point 3,3 minus both coordinates and use Pythagoras). Points 3,2 and 4,1 yield the same result: Length 1=1 unit length 2=square root 5. Length 1 = 3 unit, length 2 = square root 5.
Therefore we are looking for a point which instead yields one length which is the same length as the original. The original length was 2^2 + 2^2 = c^2 = square root 8.
If we try the point 5,1 then we get two lengths of 4 and square root 8, it forms a isosceles triangle whose base line is parallel to the x-axis.
Sorry is my explanation was confusing, it's much easier to try and draw it on a grid and visualize it. Basically the overall idea is to test the side values you get by finding the distance between the points and going with the option which results in two sides with the same length.
Hope this helped!
Answer:
D. (5,1)
Step-by-step explanation: Because it is an isosceles triangle, the next point we choose must result in two sides with the same length. This means that either the two new sides are equal, or that one of the new sides is equal to the original side. If we wanted both of the new sides to be equal, they would have to be equal distance from the new point and one of the points of the original line. However, none of the options result in both new lines being the same length.
(2,1) would result in one new length being 1 unit long (2-1 x-coordinates) and the other being square root 5 (distance from point 2,1 to point 3,3 minus both coordinates and use Pythagoras). Points 3,2 and 4,1 yield the same result: Length 1=1 unit length 2=square root 5. Length 1 = 3 unit, length 2 = square root 5.
Therefore we are looking for a point which instead yields one length which is the same length as the original. The original length was 2^2 + 2^2 = c^2 = square root 8.
If we try the point 5,1 then we get two lengths of 4 and square root 8, it forms a isosceles triangle whose base line is parallel to the x-axis.
Sorry is my explanation was confusing, it's much easier to try and draw it on a grid and visualize it. Basically the overall idea is to test the side values you get by finding the distance between the points and going with the option which results in two sides with the same length.
There are 67 questions on an exam. If you miss 8 of these questions your grade is _______ %.
Answer:
88%
Step-by-step explanation:
There are 67 questions on an exam
You miss 8 questions
The first step is to calculate the number of correct questions
= 67-8
= 59
Therefore the grade can be calculated as follows
= 59/67 × 100
= 0.880 × 100
= 88%
Hence the grade is 88%
I'm thinking of a number.My number is a whole number.My number is larger than 100.My number mod 17 = 9.My number is smaller than 200.What could be number be? (Give one possible answer. There are several correct answers.)
Answer:
the number could be any of these numbers (111, 128, 145, 162, 179, 196)
Step-by-step explanation:
From the given information, let the number that I'm thinking of to be p
p is > 100
p is < 200
and p = 9 (mod 17)
This implies that 17 ÷ p -9
p - 9 = 17q
here;
q is an integer
p = 9 + 17q
However,
100 < p < 200
= 100 < 9+17q < 200
= 100 - 9 < 17q < 200 -9
= 91 < 17q < 191
Dividing both sides by 17; we have:
= [tex]\dfrac{91}{17}< q < \dfrac{191}{17}[/tex]
= 5.45 < q < 11.24
thus the possible values of q are between 6,7,8,9,10 and 11
The possible values of p can now be:
p = 9 +17(q)
p = 9+17(6), 9+17(7), 9+17(8), 9+17(9), 9+17(10), 9+17(11)
p = 111, 128, 145, 162, 179, 196
Therefore, the number could be any of these numbers (111, 128, 145, 162, 179, 196)
The measures of two supplementary angles are 8w + 58 and 16w + 14. Find the measures of the angles
Answer:
34
Step-by-step explanation
How do you breakdown the quotient for 814÷3.7
Answer:
move the decimal to the end and add a zero to 814 i think
Step-by-step explanation:
Simplify. 1/3(1−1/4)^2 please
Answer:
3/16
Step-by-step explanation:
1/3(1-1/4)^2
1/3(3/4)^2
1/3(9/16)
3/16
Answer:
[tex]\huge \boxed{\frac{3 }{16}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{3} (1-\frac{1}{4} )^2[/tex]
Solving for brackets:
[tex]\displaystyle \frac{1}{3} (\frac{4}{4} -\frac{1}{4} )^2[/tex]
[tex]\displaystyle \frac{1}{3} (\frac{3}{4} )^2[/tex]
Squaring the fraction:
[tex]\displaystyle \frac{1}{3} (\frac{3^2 }{4^2 } )[/tex]
[tex]\displaystyle \frac{1}{3} (\frac{9 }{16} )[/tex]
Multiplying the fractions:
[tex]\displaystyle \frac{1 \times 9 }{3 \times 16}[/tex]
[tex]\displaystyle \frac{9 }{48}[/tex]
Simplifying the fraction:
[tex]\displaystyle \frac{3 }{16}[/tex]
[tex]\rule[225]{225}{2}[/tex]
12. Determine whether the given number belongs
to each set.
te?
Whole
Numbers
Integers
Rational
Numbers
es
- 34
Answer:
The number -34 belongs to:
✔️Integers and
✔️Rational numbers
Step-by-step explanation:
-34 is an integer because it can written without a fractional or decimal part.
Rational numbers are said to numbers that can actually be expressed as a fraction with integers. They have no fractional part.
For example, −34 is a rational number because it can be written as - 34/1.
-34 can be expressed as -34/17, given an integer.
-34 is NOT a whole number because whole numbers are positive numbers.
if a point is located on the x-axis , what is the y coordinate?
0
Step-by-step explanation:
im only saying this because im assuming it is on the line of the axis
Answer:
0
both x and y are zero so the y axis is 0 then the x axis is 0
Need to know asap. If m<8=23°, find the measure of each missing angle. Give your reasoning.
Answer:
157
23
157
23
157
23
157
Step-by-step explanation:
a straight line is 180 degrees. angle 8 is 23 degrees. we want to know the rest of the angles measures. 180-23=157. angles directly across the vertex are the same measure. and since the lines are parallel 2,4,6,and 8 all have the same measure and 1,3,5,and 7 have the same measure.
look at attached photo
I’m not understanding this question at all. WILL GIVE BRAINLY!! (6 is not the answer)
Answer:
-8.
Step-by-step explanation:
Substitute BC with the -4 and 2, as you were given those values to substitute with B and C. Multiply those two values. You get -8.
Can someone please help the question is below thank you!
Answer:
you just times the number buy 9 and 3 then divid by 3
Step-by-step explanation:
what is the distance between -11 and 8 on the number line?
Answer:
= 3
Step-by-step explanation:
| 11-8 |= | 3 |= 3
25×3/5×1/12 Multiply and simplify
[tex]25 \times \frac{3}{5} \times \frac{1}{12} = [/tex]
[tex]5 \times \frac{3}{1} \times \frac{1}{12} = [/tex]
[tex]5 \times \frac{1}{1} \times \frac{1}{4} = [/tex]
[tex]5 \times 1 \times \frac{1}{4} = [/tex]
[tex]5 \times \frac{1}{4} = [/tex]
[tex] \frac{5}{4} = 1 \frac{1}{4} [/tex]
Thank you.
Answer:
1.25
Step-by-step explanation:
We can start by multiplying the top part of the fraction. On the top, we have 25, 3, and 1. 25x3x1=75
Now we do the bottom. We have 5 and 12. 5x12=60
Now that we have both parts, we put it back into the fraction.
75/60
75/60=1.25
A football field is 120 yards by 53.333 yards. What is the area of the football field in acres if 1 acre
Answer:
Area in acres = 1.322 acre (Approx)
Step-by-step explanation:
Given:
Length of field = 120 yards
Width of field = 53.333 yards
Finds:
Area in acres
Computation:
1 acre = 4840 square yard
Area = 120 × 53.333
Area = 6,399.96 yard² = 6,400 yard²
Area in acres = 6,400 yard² / 4840
Area in acres = 1.322 acre (Approx)
plane. Explain your reasoning.
MOVIES An online DVD rental company charges $15 a month for unlimited rentals. Determine whether the total paid after each month is
proportional to number of months by graphing on the coordinate plane. Explain your reasoning.
In
hu
Oa. No, because the graph of the line does not pass through the origin.
Ob. Yes, because the graph is a straight line that passes through the origin.
Oc. No, because the graph of the line passes through the origin.
Od. Yes, because the graph is a straight line that does not pass through he origin.
hu
Thu
"hu
es
Res
Answer: Yes, because the graphic is a straight line that passes the through the origin.
Step-by-step explanation: Ik the answer because I have the answer key.
Help me please!!!!!!!!!!!!!
Answer:
x = 12
Step-by-step explanation:
Given that AB = 2, AD = x, BC = 2, CD = -16 + 2x, since A, B, C, D are said to be collinear, therefore:
AB + BC + CD = AD
2 + 2 + (-16 + 2x) = x
Use this equation to solve for x
2 + 2 - 16 + 2x = x
-12 + 2x = x
Subtract 2x from both sides
-12 + 2x - 2x = x - 2x
-12 = -x
Divide both sides by -1
[tex] \frac{-12}{-1} = \frac{-x}{-1} [/tex]
12 = x (negative cancels negative)
x = 12
Find all values of c such that f is continuous on (-[infinity], [infinity]). f(x) = { 3 - x^2 x less than or equal to c x, x > ca. c = -1 + squareroot 13/2, -1 - squareroot 13/2.b. c = 0. c. c = -1 = squareroot 13/2.d. c = 2.e. c = -1 + squareroot 13/2, 1 - squareroot 13/2.
Answer:
a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]
Step-by-step explanation:
The idea for the solution of this equation is to find the value of c where both parts of the piecewise-defined function are the same. So we need to take the parts of the function and set them equal to each other, so we get:
[tex]3-x^{2}=x[/tex]
and then solve for x. We move everything to one side of the equation so we get:
[tex]x^{2}+x-3=0[/tex]
and we use the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
and we substitute:
[tex]x=\frac{-1\pm \sqrt{(1)^2-4(1)(-3)}}{2(1)}[/tex]
and solve
[tex]x=\frac{-1\pm \sqrt{1+12}}{2}[/tex]
[tex]x=\frac{-1\pm \sqrt{13}}{2}[/tex]
so our two answers are:
a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]
given g(x)=x^2 and h(x)= x-3 find (g ∘ h)(x)
Answer:
(g ∘ h)(x) = x² - 6x + 9Step-by-step explanation:
g(x) = x²
h(x) = x - 3
To find (g ∘ h)(x) substitute h(x) into g(x) that's for every x in g(x) replace it with h(x)
That's
(g ∘ h)(x) = ( x - 3)²
= x² - 3x - 3x + 9
We have the final answer as
(g ∘ h)(x) = x² - 6x + 9Hope this helps you
A small apple weighs 4.5 ounces. If it is divided into 4 equal pieces, how much does each piece weigh?
SOMEONE please help me!!! pls pls pls!!!
it is true because 14 is 1/14
MULTIPLE CHOICE QUESTION
What type of exponent needs absolute value bars?
link
odd
even
Answer:
even
Step-by-step explanation:
If f(x) = 2x + 3 for all values of x, what is the value of f(-3)? A 0 B -3 C 5 D 9
Answer:
[tex]f(-3)=-3[/tex]
Step-by-step explanation:
[tex]f(x)=2x+3[/tex]
[tex]f(-3)=2(-3)+3[/tex]
[tex]f(-3)=-6+3[/tex]
[tex]f(-3)=-3[/tex]
Hope this helps!
(Please mark Brainliest!)
Which graph shows the solution of the following system of inequalities :
F
G
H
J
What's the difference between 2x+2 and 2x+2=10?
Answer:
10Step-by-step explanation:
Given both expression
2x+2 and
2x+2=10
the difference inlvosves basically the subtraction of one expression from the other expression.
now before we perform the subtraction operation, let us do some preprocessing.
let us equate the first and second expression to zero
2x+2=0 and
2x+2-10=0
we can now subtract
(2x+2)-(2x+2-10)=0
open bracket
2x+2-2x-2+10=0
collect like terms
2x-2x+2-2+10=0
0+0+10=0
the answer is 10
Ben works at a mobile phone store, where he earns a flat $80 for each 8-hour shift. He also earns a commission of $20 for each phone that he sells. If e stands for Ben's earnings and m is the number of mobile phones he sells, which of the following equations describes the amount of money that he earns in one shift? Question 6 options: A) e = m + 100 B) e = 20m + 80 C) e = –20m + 80 D) e = m + 80
Answer:
b
Step-by-step explanation:
he makes 80 dollars for a normal shift
20 dollars for every phone he sells 20m
and e is the total amount
e=20m+80
Bill has a container that is shaped like a cube. He uses 125 cubes with a side length of 1 inch to fill the container completely. What is the edge length of the container? *****Hint: 1 inch cubes to fill a container is the volume of the cube Please answer quickly!!! Thank you.
Answer:
5 inches
Step-by-step explanation:
Given
Length of a cube = 1 inch
Required
Determine the edge length of the cube
If the container can take 125 cubes, then that's the volume
So:
[tex]Volume = 125in^3[/tex]
Volume of a cube is calculated as thus;
[tex]Volume = Length^3[/tex]
This gives;
[tex]Length^3 = 125[/tex]
Take cube root of both sides
[tex]Length = \sqrt[3]{125}[/tex]
[tex]Length = 5[/tex]
Hence, the length is 5 inches