Answer:
[tex](-\frac{3}{8},2)[/tex]
Step-by-step explanation:
Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y. That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8). Our k value is 5/8. Now we will find the rise and run values which is the slope of this line segment:
[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]
Coordinates are found in this formula:
[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]
Filling that in:
[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]
which simplifies to
[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]
which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]
What is the y-value of the vertex of the function f(x) = –(x – 3)(x + 11)?
The y-value of the vertex is
.
Answer:
49
Step-by-step explanation:
Given
f(x) = - (x - 3)(x + 11)
Find the zeros by setting f(x) = 0, that is
- (x - 3)(x + 11) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 11 = 0 ⇒ x = - 11
The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros
[tex]x_{vertex}[/tex] = [tex]\frac{3-11}{2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4
Substitute x = - 4 into f(x) for y- coordinate of vertex
f(- 4) = -(- 7)(7) = 49 ← y- value of vertex
A company launches 4 new products. The market price, in dollars, of the 4 products after a different number of years, x, is shown in the following table:
Product Function Year 1
(dollars) Year 2
(dollars) Year 3
(dollars)
Product 1 f(x) = 4x + 8 12 16 20
Product 2 g(x) = 2^x 2 4 8
Product 3 h(x) = x^2 + 12 13 16 21
Product 4 j(x) = x^3 1 8 27
Based on the data in the table, for which product does the price eventually exceed all others?
Product 1
Product 2
Product 3
Product 4
It’s product two right???
Product 4 after the third year is 27 which is higher than the rest after 3 years.
And because x is raised to the third, the amount would Increase by being raised to the 3rd every year.
The answer is Product 4.
Please help me out with this
Answer:
6 in^2.
Step-by-step explanation:
The area of 2 similar figures are in the ratio of the squares of corresponding sides. So we have the equation:
3^2 / 6^2 = x / 24
9/36 = x /24
1 / 4 = x / 24
x = 24/4 = 6 in^2 (answer).
On a snack tray there are 3 different types of crackers ( a dozen of each) and six different types of cheese ( a half dozen cubes of each). how many different combinations can be made.
Answer:
18 combinations
Step-by-step explanation:
Assuming you can only have one slice of cheese per cracker, then you would have to multiply the number of types of crackers by how many types of cheeses there are to find the total amount of combinations.
3 crackers * 6 cheeses = 18 combinations
40 Points Please Help I'm not sure if they are correct.
Distance Formula:
D=(x2 −x1 )^2 +(y2 −y1 )^2
1. Find the distance between (0,0) and (6,8)?
2. Find the distance between (-3,2) and (3,5)?
3. Find the distance between (-1,-1) and (4,-5)?
Replace the x and y values in the given equation.
1. d = √((6-0)^2 + (8-0)^2
= √(6^2 + 8^2)
= √(36 + 64)
= √100
= 10
2. d = √((3-(-3))^2 + (5-2)^2
=√((3+3)^2 + 3^2)
=√(6^2 + 3^2)
= √(36 + 9)
= √45
=3√5 ( exact ) or as a decimal 6.7082 (round as needed)
3. d = √((4-(-1))^2 + (-5-(-1))^2
= √((4+1)^2 + (-5+1)^2)
= √(5^2 + -4^2)
=√(25 + 16)
= √41 (exact) or as a decimal 6.4031 (round as needed)
The height of a right rectangular prism is three times the
width of the base. The length of the base is twice the width.
Which expression represents the volume of the prism in
terms of w, the width of the base?
6 II
O5w2 cubic units
O6w2 cubic units
O 5w cubic units
O6wº cubic units
Answer:
6w³ cubic units
Step-by-step explanation:
The volume of a right rectangular prism is the product of its dimensions:
V = LWH
= (2w)(w)(3w) = 6w³ . . . . cubic units
Answer:
6*W^3 cubic units
Step-by-step explanation:
Right rectangular prism volume (V) is calculated as
V = L*W*H
where L is length, W is width and H is height
The height is three times the width of the base means
H = 3*W
The length of the base is twice the width means
L = 2*W
Replacing in volume formula
V = 2*W*W*3W
V = 6*W^3
Two years after it’s purchase, if Manuel’s gift card is unused, the automatic decrease on the gift card balance is given by the equation b = 50 - 5m, where m is the number of months beyond two years.
Is this model of the siu action linear? If it is, what are the slope and y-intercept?
A. linear: slope = -10, y-intercept = 5
B. linear: slope = -50, y-intercept = 5
C. linear: slope = -5, y-intercept = 50
D. not linear
Answer:
Option C. linear: slope = -5, y-intercept = 50
Step-by-step explanation:
Let
b ----> is the automatic decrease on the gift card balance
m ----> is the number of months beyond two years
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
In this problem the linear equation that represent this situation is
[tex]b=-5m+50[/tex] ---> equation of the line into slope intercept form
so
The slope is -5
The y-intercept is 50
Answer:
This function is linear. True
The slope of this function is 50. False
The y-intercept of this function is 50. True
The equation yˆ=24.387x + 328.182 models Math SAT scores, y, where x is the number of hours spent studying.
What does the y-intercept of the equation represent in the context of the situation?
The average number of hours studied is about 328.
Without any studying, the score would be about 328.
Without any studying, the score would be about 24.
The average number of hours studied is about 24.
Answer:
Without any studying, the score would be about 328
Step-by-step explanation:
The y-intercept of an equation represents the point where its graph crosses the y-axis. At this point the value of x is always equal to 0.
The y-intercept of the equation in this context would represent the Math SAT score of a student who did not do any studying, that is the number of hours spent studying, x = 0.
Substitute x = 0 in the given equation and solve for y;
y = 24.387(0) + 328.182
y = 328.182
Therefore, Without any studying, the score would be about 328
Joanne divided 14 of a pastry into 3 equal pieces. Which fraction of the original pastry represents each of the 3 pieces Joanne cut?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Note Is a 1/4 of a pastry instead of 14 of a pastry
we know that
To find the fraction of the original pastry that represents each of the 3 pieces cut by Joanne, divide 1/4 by 3
so
[tex](1/4)/3=\frac{1}{12}[/tex]
Answer:
1/12
Step-by-step explanation:
What is the y-coordinate of the point of intersection for the two lines given below?
A: 4
B: -14
C: -3
D: -2
Answer:
B. -14
Step-by-step explanation:
If you solve the system using the method of elimination, the y terms will automatically cancel each other out without any manipulation at all. So go with it and solve for x first. If the y terms cancel out, you're left with x = -3.
If x = -3, sub that value in for x in eitheer one of the original equations and solve for y:
[tex]3x-y=5[/tex] becomes
[tex]3(-3)-y=5[/tex] and
[tex]-9-y=5[/tex] so
[tex]y=-14[/tex]
HELP DO NOT UNDERSTAND THIS QUESTION AT ALL THE BEST ONE WILL BE MARKED AS BRAINLIEST
Step-by-step answer:
A line with slope (or gradient) m, passing through a point (x0,y0) can be represented by the equation:
(y-y0) = m(x-x0) ......................(1)
Here,
(x0,y0) = (1,7), and
slope/gradient = -2
Substitute values into (1) above gives
(y-7)=2(x-1)
Expand and simplify
y-7 = 2x-2
y =2x -2 + 7
y=2x+5
is the final answer.
Find an explicit rule for the nth term of the sequence.
-4, -8, -16, -32, ...
Select one:
a. an = -4 • 2n - 1
b. an = 2 • -4n + 1
c. an = 2 • -4n
d. an = -4 • 2n
Answer: -4 . 2ⁿ⁻¹
Step-by-step explanation: This is a geometric progression
the nth term is given by arⁿ⁻¹
a = the first term of the sequence
r = common ratio
n= number of terms
for this sequence
a = -4
r = -8/-4 = 2
nth term, an = -4 . 2ⁿ⁻¹
Answer:
an = 2 ● (-4)n-1
Step-by-step explanation:
Just got it right
Find the surface area of the composite solid.
Answer:
Option B is correct.
Step-by-step explanation:
Given:
A Solid Figure made up pf cuboid and a triangular based prism.
To find: Total Surface area of the figure.
Total Surface Area = Area of front + Area of top + Area of Back + 2 × Area of side + Area of bottom
Area of Front = Area of Square + Area of rectangle
= 10 × 10
= 100 in.²
Area of top = Area of Rectangle
= 13 × 10
= 130 in.²
Area of back = Area of square in down + Area of rectangle in up
= 10 × 10 + 5 × 10
= 100 + 50
= 150 in.²
Area of the bottom = Area of the rectangle
= 12 × 10
= 120 in.²
Area of the side = Area of rectangle + Area of the triangle
= 12 × 10 + 1/2 × 5 × 12
= 120 + 5 × 6
= 120 + 30
= 150 in.²
Total Surface Area = 100 + 130 +150 + 120 + 2 × 150
= 500 + 300
= 800 in.²
Therefore, Option B is correct.
Evaluate d^2y/dx^2 for 2x^2+2y=17
Answer:
d^2y/dx^2 = 2
Step-by-step explanation:
We take the derivative with respect to x twice here. Find the first derivative, simplify the results and then differentiate that result again with respect to x.
(d/dx)(2x^2+2y=17+ → 4x + 2(dy/dx) = 0. Simplifying, we get:
dy/dx = -2x
Now take the derivative of this new equation, obtaining:
d^2y/dx^2 = 2
A motorboat takes 5 hours to travel 500 km up stream the return trip takes 4 hours going down stream. What is the rate of the boat in still water? And what is the rate of the current
Answer: 25 km
Step-by-step explanation:
500 km / 5 = 100 km up stream
500 km / 4 = 125 km down stream
125 - 100 = 25 km in still water
Given that f(x) is the original function, what is true about the transformation, g(x)? g(x) is reflected about the y-axis. g(x) is reflected about the y-axis and shifted up by 4 units. g(x) is reflected about the x-axis. g(x) is reflected about the x-axis and shifted up by 4 units.
Answer:
C
GX is reflected across the X-axis
g(x) is reflected across the X-axis if f(x) is the original function.
What is function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here we have f(x) is the original function, the true value of g(x) is that g(x) is reflected across the X-axis.
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Last week at best bargain, 75% of the computers sold were laptops. If 340 computers were sold last week, how many laptops were sold?
Answer:
255
Step-by-step explanation:
1. 75% is actually 0.75, and you want to find 75% of 340.
2. Multiply 0.75 and 340. 0.75 x 340 = 255
3. Answer = 255
What is the probability of randomly selecting an odd number from the numbers 1-15
Answer:
7/15
Step-by-step explanation:
odd numbers are those that do not have divides ie1,2,3,5,7,11,13
The probability of randomly selecting an odd number from the numbers 1-15 is 8/15.
What is the probability?
Probability is used to know the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that a randomly selected number would be odd = number of odd numbers / total numbers
Odd numbers between 1 and 15 = 1 , 3, 5, 7, 9, 11, 13, 15
Probability that a randomly selected number would be odd = 8/15
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When Frank buys three packs of pens, he knows he has 36 pens. When he buys five packs, he knows he has 60 pens. What is the constant of proportionality between the number of packs and the number of pens?
Answer:
The answer is 12. There are 12 pens in each pack.
Step-by-step explanation:
The constant of proportionality between the number of packs and the number of pens that Frank buys is 12 pens per pack, calculated by dividing the total pens by the number of packs in both given scenarios.
The student asks about the constant of proportionality between the number of packs of pens and the number of pens. To find this, we divide the number of pens by the number of packs for each given scenario to ensure the ratio is consistent.
Given Frank buys three packs and ends up with 36 pens, we divide 36 pens by 3 packs to get 12 pens per pack.
When he buys five packs and has 60 pens, we again divide 60 pens by 5 packs and get the same result, 12 pens per pack. Therefore, the constant of proportionality is 12 pens per pack.
What is the phase shift of y = sin(1/2 x - pi/2)?
Answer:
π
Step-by-step explanation:
The standard form of the sine function is
y = a sin(bx + c)
where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and
phase shift = - [tex]\frac{c}{b}[/tex]
here b = [tex]\frac{1}{2}[/tex], c = - [tex]\frac{\pi }{2}[/tex]
phase shift = - [tex]\frac{-\frac{\pi }{2} }{\frac{1}{2} }[/tex]
= [tex]\frac{\pi }{2}[/tex] × 2 = π
You deposit 350 in an account that pays 3% annual intrest. Find the balance afer 2 years if the intrest is compounded
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$350\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=350\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=350(1.03)^2\implies A=371.315[/tex]
An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.
First, you have to find the 52% of the 30%(chance that he gets a dividend) .Then you simply have to subtract the result (15.6%) from the 30%. Your result is 14.4% chance that he wont get a divident.
Answer:
14.4%
Step-by-step explanation:
An investment advisor believes that there is a 30% chance of making money by investing in a specific stock. If the stock makes money, then there is a 52% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money but does not receive a dividend.
Probability is the chance/likelihood that an event will occur or not
The chances that one makes money from a stock is 30%
Chances that one will not=70%
Chances that there will dividend among those who made money is =52%
chances that there wont be dividend is =100%-52%=48%
the probability that One will make money and not receive a dividend
is 30%*(100%-52%)
14.4%
How do you solve simple interest
$600 at 5% for 2 years
and
%1500 at 4% for 4 years
Answer:
1. $60
2. $240
Step-by-step explanation:
Use the formula for simple interest. Put your numbers in the formula and do the arithmetic.
i = Prt . . . . where i is the interest amount, P is the principal, r is the rate, t is the time period
1. P = $600, r = 0.05, t = 2, so you have ...
i = $600·0.05·2 = $60
__
2. P = $1500, r = 0.04, t = 4, so you have ...
i = $1500·0.04·4 = $240
1. y ≤ 3x − 4
2. y ≠ 2x
3. y > x + 5
4. y < 0.5x −3
5. y ≥ 4x +2
6. 5x + y < 5
All answers sums up only one question on test. If answered correctly will marked for brainlest. Thanks !!
Answers:
1. x[tex]\geq[/tex] [tex]\frac{y+4}{3}[/tex]
2. x [tex]\neq[/tex][tex] \frac {y} {2} [/tex]
3. x<y-5
4. x>2(y+3)
5. x [tex]\leq[/tex] [tex]\frac{y-2}{4}[/tex]
6. x < [tex]\frac{5-y}{5}[/tex]
Make me brainiest!!!!!!!!!!
Answer:
Step-by-step explanation:
1. x\geq\frac{y+4}{3}
2. x \neq \frac {y} {2}
3. x<y-5
4. x>2(y+3)
5. x \leq\frac{y-2}{4}
6. x < \frac{5-y}{5}
Graph 3x2 + 3y2 = 75
Answer:
See attachment
Step-by-step explanation:
The given equation is:
[tex]3x^2+3y^2=75[/tex]
We divide through by 3 to obtain;
[tex]x^2+y^2=25[/tex]
This is rewritten as:
[tex]x^2+y^2=5^2[/tex]
This is the equation of a circle centered at the origin with radius 5 units.
A vegetable and a surrounding path are shaped like a square that together are 11 ft wide. The path is 2 feet wide. If one bag of gravel covers 9 square feet, how many bags are needed to cover the path?
Answer:
8 bags
Step-by-step explanation:
The area of the path is equal to the area of the overall square minus the area of the garden.
Area of a square is the side length squared:
A = s²
The overall square has a side length of 11 feet. The side length of the garden is 11 - 2 - 2 = 7 feet. So the area of the path is:
A = 11² - 7²
A = 121 - 49
A = 72
The area of the path is 72 ft². If one bag of gravel covers 9 ft², then the number of bags needed is:
72 ft² × (1 bag / 9 ft²) = 8 bags
Nine lollies cost less than $10, while ten lollies cost more than $11 how much does each lollipop cost?
$21 it will cost for lollipop
Answer:
$1.10
Step-by-step explanation:
1.10 times 10
Please help me find the area of the triangular prism. and show the work please
Answer: 36 in²
Step-by-step explanation:
You can calculate the area of this right prism by adding the area of its faces.
You can observe that the faces of the right prism are: Three different rectangles and two equal triangles.
The formula for calculate the area of a rectangle is:
[tex]A=lw[/tex]
Where "l" is the lenght and "w" is the width.
The formula for calculate the area of a triangle is:
[tex]A=\frac{bh}{2}[/tex]
Where "b" is the base and "h" is the height.
You can observe that the hypotenuse of the each triangle is the length of the larger rectangle, then , you can find its value with the Pythagorean Theorem:
[tex]a=\sqrt{b^2+c^2}[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.
Then, this is:
[tex]a=\sqrt{(4in)^2+(3in)^2}=5in[/tex]
Therefore, you can add the areas of the faces to find the area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:
[tex]A=(2in)(5in)+(3in)(2in)+(4in)(2in)+2(\frac{3in*4in}{2})=36in^2[/tex]
Three Friends are starting a food truck and a contributing a total of 140,000 to begin operations. Their investments are in the ratio of 2:5:7. What is the difference in investment betweenThe smallest investor and the largest Al smallest investor and the largest inverstor
Answer:
Step-by-step explanation:
The sum of those numbers is 14. Let's divide 14000 by 14 to get the number of parts (each part will be an investment in dollars) and we get 10,000. So if a person invests 2 parts, he invests 2(10,000). A person that invests 5 parts invests 5(10,000), and likewise for the person investing 7 parts: 7(10,000). That gives us 20,000 + 50,000 + 70,000 = ?
(140,000)
The difference in investment between the largest and the smallest is 50,000
Final answer:
To find out the investments of three friends in a ratio of 2:5:7, one part is calculated as $10,000. The smallest investor contributes $20,000 and the largest investor contributes $70,000. Hence, the difference in their investments is $50,000.
Explanation:
The question is asking to determine the individual investments of three friends in a food truck business based on their total contributions amounting to $140,000 and the ratio of their investments being 2:5:7. First, we find the total number of parts in the ratio (2+5+7=14 parts). To find the value of one part, we divide the total investment by the number of parts ($140,000 \/ 14 = $10,000 per part).
Now, we can calculate each friend's investment:
The difference in investment between the smallest and the largest investor is $70,000 - $20,000 = $50,000.
Julius is buying beverages for brunch. He needs to buy a total of 5 gallons of beverages. He decides to buy two containers of each beverage. How many gallons of beverages did he buy? pick two
2 pints of milk
2 quarts of orange juice
16 cups of chocolate milk
32 ounces of lemonade
Julius bought a total of 2 gallons of beverages, including 2 quarts of orange juice and 16 cups of chocolate milk.
To find out how many gallons of beverages Julius bought, we need to convert each quantity to gallons and then sum them up:
1. **2 pints of milk**:
- 1 pint = 0.125 gallons
- 2 pints = [tex]\(2 \times 0.125 = 0.25\)[/tex] gallons
2. **2 quarts of orange juice**:
- 1 quart = 0.25 gallons
- 2 quarts = [tex]\(2 \times 0.25 = 0.5\)[/tex] gallons
3. **16 cups of chocolate milk**:
- 1 cup = 0.0625 gallons
- 16 cups =[tex]\(16 \times 0.0625 = 1\)[/tex] gallon
4. **32 ounces of lemonade**:
- 1 ounce = 0.0078125 gallons
- 32 ounces = [tex]\(32 \times 0.0078125 = 0.25\)[/tex] gallons
Now, let's sum up the quantities:
[tex]\[ 0.25 + 0.5 + 1 + 0.25 = 2 \][/tex]
So, Julius bought a total of 2 gallons of beverages.