Final answer:
The x-intercept of the line 5x - y = 10 is (2, 0), the y-intercept of the line 9x + 3y = -18 is (0, -6), and the equation 6x - 4y = -12 has an x-intercept at (-2, 0) and a y-intercept at (0, 3).
Explanation:
To find the x-intercept of a line, we set the value of y to zero and solve for x. For the equation 5x - y = 10, we set y to 0:
5x - (0) = 10
5x = 10
x = 2
The x-intercept is therefore the point (2, 0).
To find the y-intercept of a line, we set the value of x to zero and solve for y. For the equation 9x + 3y = -18, we set x to 0:
(0) + 3y = -18
3y = -18
y = -6
The y-intercept is therefore the point (0, -6).
For the equation 6x - 4y = -12, the x-intercept and y-intercept can be found similarly. Let's start with the x-intercept. Set y to 0:
6x - (0) = -12
6x = -12
x = -2
The x-intercept is the point (-2, 0). Now, for the y-intercept, we set x to 0:
(0) - 4y = -12
-4y = -12
y = 3
The y-intercept is the point (0, 3). Thus, for 6x - 4y = -12, the intercepts are x = -2 and y = 3.
If the circumference of a circle is 21.98cm, how much is the area?
Answer: 38.45
Step-by-step explanation:
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=21.98 \end{cases}\implies 21.98=2\pi r\implies \cfrac{21.98}{2\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi \left( \boxed{\cfrac{21.98}{2\pi }} \right)^2\implies A=\cfrac{21.98^2}{2^2\pi }\implies A\approx 38.445[/tex]
The radius of the base of a right circular cone is 5 times greater than the radius of a second right circular cone. If the heights of both cones are the same, what is the volume of the larger cone divided by the volume of the smaller cone? A. 5 B. 10 C. 15 D. 25
The volume of the larger cone divided by the volume of the smaller cone is 25.
What is the ratio of the volumes?A cone is a three-dimensional object that is made up of a circular base and a vertex.
Volume of a cone = 1/3(πr²h)
Assumed dimensions of the smaller cone:
Height = 10 Radius = 3Volume = 1/3(π x 9 x 10) = 30π
Assumed dimensions of the larger cone:
Height = 10 Radius = 3 x5 = 15Volume = 1/3(π x 225 x 10) = 750π
Ratio of the volumes = 750π / 30π = 25
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Answer:
A, 25 is correct
Step-by-step explanation:
i got it right on edge 2023
which equation represents the distributive property
Answer:
u didnt give all the info
Step-by-step explanation:
Rectangle with length 8 1/2 in. And width 6in
Answer:
51 inches
Step-by-step explanation:
area = base x height
8.5 x 6 = 51
51 inches
Each cube represents 1 cubic inch. What is the volume if the prism?
Answer:
12 in³
Step-by-step explanation:
Its made up of 12 (4×3 = 12) cubes of 1 in³ each
So 12 × 1 = 12 in³
20 points!!! (PLEASE ANSWER ALL, AND ALL CORRECTLY!!) this test is already late!
At the zoo, the ratio of mammals to reptiles is 4:3. There are 20 mammals in the zoo.
(a) How many reptiles are in the zoo?
(b) If the zoo adds 12 more mammals to its collection, how many more reptiles will they have to add to keep the ratio the same?
(c) A zoo in a different city has a ratio of mammals to reptiles of 6:5. Which zoo has the larger ratio of mammals to reptiles?
Thank you!
Answer: im not sure but a)15 B)24 c)zoo in a different city
Step-by-step explanation:
There are 15 reptiles in the zoo. To keep the ratio 4:3, if the zoo adds 12 more mammals, they will need to add 9 more reptiles. The first zoo has a larger ratio of mammals to reptiles (4:3) compared to the second zoo (6:5).
To answer the question, let's solve each part step by step:
Given the ratio of mammals to reptiles is 4:3 and there are 20 mammals, we can set up a proportion to find the number of reptilesIf the zoo adds 12 more mammals, to keep the same ratio of 4:3, we calculate the number of reptiles to add. We can find this by multiplying the 12 additional mammals by 3/4, which results in 9 more reptiles.To compare the ratios of the zoos, we can turn them into comparable fractions: 4/3 for the first zoo and 6/5 for the second zoo. By finding a common denominator or comparing their cross-multiplication products, we can determine which ratio represents a larger number of mammals to reptiles. Here, 4/3 is larger than 6/5, so the first zoo has a larger ratio of mammals to reptiles. This can be confirmed by cross multiplication: 4*5=20 and 6*3=18, since 20 is greater than 18, the first zoo has a larger ratio.Simplify the expressions 4k9×8k3×k
Answer:
32k13
Step-by-step explanation:
32k13 Multiply the number add the the exponent
To simplify the expression 4k9×8k3×k, combine the coefficients and add the exponents of the same variable k to get 32k13.
Explanation:To simplify the expression 4k9×8k3×k, we can combine the coefficients and add the exponents of the same variable k.
4k9×8k3×k = (4×8)k(9+3+1) = 32k13
Therefore, the simplified expression is 32k13.
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Find the value of 6+x when x = 15.
Answer:
Step-by-step explanation:
Given the function f(x)=6+x
F(x) is dependent on x,
When x=1
f(x)=6+x
f(x)=6+1,
f(x)=7
When x=2
f(x)=6+x
f(x)=6+2
f(x)=8.
This will continue like this till we get to x=15
So when x=15
We will substitute x=15 into the function f(x)
f(x)=6+x
f(x)=6+15
f(x)=21
Then, the answer is 21.
Answer: 17
Step-by-step explanation:
To solve 6+x when x = 15,
Step 1: Substitute 15 into x
Step 2: Sum 6 and 15
6+15= 17.
Karla had $138.72 in her checking account. She wrote checks for $45.23 and $18. Then she made a deposit for 75.85 into her account.what is the best estimate for how much money is in karla’s account now
Answer:
$151.34
Step-by-step explanation:
First, Karla starts with $138.72.
Then Karla writes checks for $45.23 and $18.00. This means the money will be withdrawn, so let's subtract these from the total.
$138.72 - $45.23 - $18.00 = $75.49
Now, Karla has $75.49 in her account.
However, a $75.85 deposit is made to her account. So let's add this back to the total.
$75.49 + $75.85 = $151.34
So after all the transactions, Karla has $151.34 in her checking account.
Use the relationship between the angles in the
figure to answer the question.
Which equation can be used to find the value
of x?
Drag and drop the equation into the box.
Answer:
Depends on what x represents.
Step-by-step explanation:
Can you provide more details?
Answer:
x = 180 - (67 + 52)
Step-by-step explanation:
Had it wrong the first time ;)
The dot plot below shows 6 data points with a mean of 16.
A dot plot going from 11 to 20. 1 dot is above 12, 13, 15, 17, 19, 20.
What is the absolute deviation at 19?
Answer:I think its C
Step-by-step explanation:
Answer: the answer is c
Step-by-step explanation:
Write 6 powered 0 in positive exponents
Answer:
1
Step-by-step explanation:
Anything to the power 0 is 1
Therefore, 6^0 is 1
Answer: 1
Answer:
6^0 = 1
Step-by-step explanation:
"6 to the power 0" is 6^0 = 1
Solve for X, and graph
8. - 6x + 14 <-28 OR 9x + 15 <- 12
For this case we must indicate the solution set of the given inequalities:
[tex]-6x + 14 <-28[/tex]
Subtracting 14 from both sides of the inequality we have:
[tex]-6x <-28-14\\-6x <-42[/tex]
Dividing by 6 on both sides of the inequality:
[tex]-x <- \frac {42} {6}\\-x <-7[/tex]
We multiply by -1 on both sides, taking into account that the sense of inequality changes:
[tex]x> 7[/tex]
Thus, the solution is given by all values of x greater than 7.
On the other hand we have:
[tex]9x + 15 <-12[/tex]
Subtracting 15 from both sides of the inequality we have:
[tex]9x <-12-15\\9x <-27[/tex]
Dividing between 9 on both sides of the inequality we have:
[tex]x <- \frac {27} {9}\\x <-3[/tex]
Thus, the solution is given by all values of x less than -3.
Finally, the solution set is:
(-∞, - 3) U (7,∞)
Answer:
(-∞, - 3) U (7,∞)
What is the value of the expression 3 ^ 3 - 2 ^ 3
Answer:
27 - 8 = 19
The answer is 19.
Step-by-step explanation:
What is the inverse of f(x)= 9x-8
Answer:
f^-1(x) = (x + 8) / 9
Step-by-step explanation:
Step 1: Set y to x and x to y
y = 9x - 8
x = 9y - 8
Step 2: Solve for y
x + 8 = 9y - 8 + 8
(x + 8) / 9 = 9y / 9
(x + 8) / 9 = y
Step 3: Rename y to f^-1(x)
f^-1(x) = (x + 8) / 9
Answer: f^-1(x) = (x + 8) / 9
The inverse of the function f(x) = 9x - 8 is f^-1(x) = (x + 8) / 9.
To find the inverse of the function f(x) = 9x - 8, follow these steps:
First, replace f(x) with y. So, we have y = 9x - 8.
Next, solve for x. To do this, swap x and y to get x = 9y - 8.
Now, isolate y by adding 8 to both sides, resulting in x + 8 = 9y.
Finally, divide both sides by 9 to solve for y, giving y = (x + 8) / 9. This is the inverse function.
To denote the inverse, we replace y with f-1(x), resulting in f-1(x) = (x + 8) / 9.
Y=5x+20
Y=-7x-16
Solve each system by substitution
Answer:
x=3
y=35
Step-by-step explanation:
5x+20=-7x-16
-16+20=4
5x=-7x+4
5x+7x= 12x
12x=4
12/4=3
Answer: x = -3 ; Y = 5
Step-by-step explanation:
Y=5x+20
Y=-7x-16
5x+20 = -7x-16
5x+ 7x = -16 - 20
12x = - 36
x = -36 / 12
x = -3
Y=5x+20
Y = 5.(-3) + 20
Y = - 15+20
Y = 5
Suppose William and Donald both drive the same car, and have the same
deductible for car insurance. If William drives an average of 12,000 miles a
year and Donald drives an average of 15,000 miles a year, who is most likely
to pay a higher annual premium?
Answer: William
Step-by-step explanation: This is true because whichever has a better gas mileage pays less, so the bigger number per year has better mileage, so 15,000 would have better which is Donald, and William has 12,000 which is worse, so he would have to pay more.
Answer: Donald
Step-by-step explanation:
Find the value of the expression. x2 + y for x = 5 and y = 6
Answer:
31
Step-by-step explanation:
[tex] {x}^{2} + y \\ = {5}^{2} + 6 \\ = 25 + 6 \\ = 31 [/tex]
Answer:
31
Step-by-step explanation:
25+6=31
If f(x) = 3x5 - 5x4 + 29, find f(-1).
f(-1) = 3((-1)^5)-5((-1)^4)+29 = -3-(5)+29 = 21
answer: 21
Answer:
The value of f(-1) is 21
Step-by-step explanation:
Given:
[tex]f(x) = 3x^5 - 5x^4 + 29[/tex]
Finding f(-1)
[tex]f(-1)=3(-1)^5-5(-1)^4+29\\\\[/tex]
Multiplying '-1' odd times gives -1 and even times gives '1'
[tex]f(-1)=3(-1)-5(1)+29\\\\f(-1)=-3-5+29\\\\f(-1)=-8+29\\\\f(-1)=21\\[/tex]
The value of f(-1) is 21
2). A bag contains 50 pieces of gum flavored cherry, grape, and watermelon.
• William will randomly pick a piece of gum.
• The probability of picking cherry is 5.
• The probability of picking watermelon is 10.
3
What is the probability William will pick a piece of grape gum?
Answer:
37 (i think)
Step-by-step explanation:the probability means the amount of (in this case) the cherry gum or watermelon gum. Add the amount and then subtract the total from the WHOLE number of the WHOLE of the group
(hopefully that made sense)
What is 5y-4x =-7
2y+4x=14
X=?
Y=?
Answer:
X=3
Y=1
Step-by-step explanation:
In solving simultaneous equations, there are three methods, we have the elimination method, substitution method or graphical method. But for the purpose of this question, we would be using Elimination method.
5y-4x =-7 Equation 1
2y+4x=14 Equation 2
Since x has the same coefficient, it's easy to eliminate by adding up the two equations
5y+2y=7y
-4x+(+4x)=0
-7+(+14)=7
We have 7y=7
Divide both sides by 7,
y=7/7
y=1
Substituting for y in equation 2.
2(1)+4x=14
2+4x=14
4x=14-2
4x=12
x=12/4
x= 3
solve -5 + w/3 = -1
12
-12
2
-2
Answer:
Option A, 12
Step-by-step explanation:
Step 1: Add 5 to both sides
-5 + w/3 + 5 = -1 + 5
w / 3 = 4
Step 2: Multiply both sides by 3
w/3 * 3 = 4 * 3
w = 12
Answer: Option A, 12
Calculate the length of AB using Sine rule
Answer:
Approximately [tex]22.2\; \rm m[/tex].
Step-by-step explanation:
By sine rule, the length of each side of a triangle is proportional to the sine value of the angle opposite to that side. For example, in this triangle [tex]\triangle ABC[/tex], angle [tex]\angle A[/tex] is opposite to side [tex]BC[/tex], while [tex]\angle C[/tex] is opposite to side [tex]AB[/tex]. By sine rule, [tex]\displaystyle \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C}[/tex].
It is already given that [tex]BC = 22.4\; \rm m[/tex] and [tex]\angle A = 58^\circ[/tex]. The catch is that the value of [tex]\angle C[/tex] needs to be calculated from [tex]\angle A[/tex] and [tex]\angle B[/tex].
The sum of the three internal angles of a triangle is [tex]180^\circ[/tex]. In [tex]\triangle ABC[/tex], that means [tex]\angle A + \angle B + \angle C = 180^\circ[/tex]. Hence,
[tex]\begin{aligned}\angle C &= 180^\circ - \angle A - \angle B \\ &= 180^\circ - 58^\circ - 65^\circ \\ &= 57^\circ\end{aligned}[/tex].
Apply the sine rule:
[tex]\begin{aligned} & \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C} \\ \implies & AB = \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \end{aligned}[/tex].
[tex]\begin{aligned}AB &= \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \\ &= \frac{22.4\; \rm m}{\sin 58^\circ} \times \sin 57^\circ \\ &\approx 22.2\; \rm m\end{aligned}[/tex].
Name the coordinates of the points on the graph.
F
G
H
M
P
Answer:
Is their a picture so we can see where to put it
Tiffany answered 80% of the questions on her math test correctly. There were 40 questions. How many questions did Tiffany get correctly
write 16% as a decimal and reduced fraction
i need help
16% = 0.16 = [tex]\frac{4}{25}[/tex]
Step-by-step explanation:
Given,
16%
We need to find out the decimal and reduced fraction.
Decimal Fraction
16% = [tex]\frac{16}{100}[/tex] = 0.16
Reduced Fraction
16% = [tex]\frac{16}{100}[/tex] = [tex]\frac{4}{25}[/tex] [ Diving both by 4]
Answer:
0.16 as a decimal
4/25 as a reduced fraction
Step-by-step explanation:
16%
A percentage is an hundred. Hence, the percentage of any number is that number divided by 100.
16% will therefore be 16/100
To decimal form gives 0.16
To a reduced fraction, we have
16/100
Using 2 to reduce
8/50
Using 2 to reduce again
4/25
It can't be reduced with a common number again.
Write an equation that represents the volume V as a function of the height h
Answer:
h=V/b
Step-by-step explanation:
The volume V can be represented as a function of height h by the equations V = lwh for a rectangular prism or V = πr²h for a cylinder. If other dimensions are constants, this can be simplified to V=k*h, where k represents the base area.
Explanation:To represent the volume V as a function of the height h, we typically consider the volume of a rectangular or cylindrical shape. The volume V of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. If we consider a cylinder, the volume is given by the equation V = πr²h, where r is the radius of the base circle and h is the height. However, if we simplify this formula assuming only the height can vary and all other dimensions are constants, the function could be simplified to V=k*h, where k represents the area of the base.
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What is the area of this trapezoid
Answer:
[tex]A = 80[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
Given Data:
a = 7+3+7 =17 units
b = 3 units
h = 8 units
To Find Out:
Area of trapezoid = ?
Formula:
[tex]A = \frac{a+b}{2}h[/tex]
Solution:
[tex]A = \frac{a+b}{2}*h[/tex]
[tex]A = \frac{17+3}{2}*8[/tex]
[tex]A = \frac{20}{2}*8[/tex]
[tex]A =10*8[/tex]
[tex]A = 80[/tex] [tex]units^{2}[/tex]
The lengths of the three sides of a triangle are given. Classify each triangle as acute, right or
obtuse.
30, 40, 50
1)
Triangle with side lengths 30, 40, and 50 is a right triangle.
To classify the triangle based on the lengths of its sides, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For the given lengths of sides:
[tex]\(a = 30\)[/tex]
[tex]\(b = 40\)[/tex]
[tex]\(c = 50\)[/tex]
We can check if the triangle is a right triangle:
[tex]\[c^2 = a^2 + b^2\][/tex]
Substituting the values:
[tex]\[50^2 = 30^2 + 40^2\][/tex]
[tex]\[2500 = 900 + 1600\][/tex]
[tex]\[2500 = 2500\][/tex]
Since [tex]\(2500 = 2500\)[/tex], the Pythagorean theorem holds true, meaning this triangle is a right triangle.
So, the given triangle with side lengths 30, 40, and 50 is a right triangle.
LaTanya says that the growth factor of f(x) = 100(1.25) is 25%. What mistake did LaTanya make?
Answer:
The first error consists in the multiplication of f (x) = 100 * (1.25), the value she mentions is incorrect since it is 125.
It would be a 125% increase really.
In order for LaTanya's phrase to have no error she had to mention that it was a 25% increase over the original amount, in this way, the phrase would make sense and be valid.
Answer:
LaTanya confused growth factor with growth rate. The growth factor is 1.25. The growth rate is 25%.
Step-by-step explanation:
In the exponential growth model,
f(x)=a(1+r)x
a is the inital amount, r is the growth rate, and (1+r) is the growth factor. Hence, the growth factor of the given function is 1.25.