Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.) 5x + 4y = 24 2x – 7y = 26 7x – 3y = 50 7x + 3y = 50 3x - 3y = -2 36 x+ 11y = -2

Answers

Answer 1

Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.)

5x + 4y = 24

2x – 7y = 26

____

a) 7x – 3y = 50

b) 7x + 3y = 50

c) 3x - 3y = -2

d) 3 x+ 11y = -2​

_____________________________

Try adding and subtracting the equations

5x + 4y = 24

+(2x – 7y = 26)

_______________

7x -3y= 50

5x + 4y = 24

-2x + 7y = -26

______________

3x + 11y = -2

Do you have any questions regarding the solution?


Related Questions

For each ordered pair, determine whether it is a solution to 7x - 4y = -5.(x,y)(-2,6) it is a solution yes or no(1,3) it is a solution yes or no(-3,4) it is a solution yes or no(4,2) it is a solution yes or no

Answers

If x=1, then:

[tex]\begin{gathered} 7(1)-4y=-5 \\ \Rightarrow-4y=-5-7=-12 \\ \Rightarrow y=\frac{-12}{-4}=3 \\ \\ y=3 \end{gathered}[/tex]

therefore, a solution to the equation 7x-4y=-5 is (1,3)

Hi! I was absent today and did not understand this lesson please I will be really grateful if you help me ! I appreciate it this is classwork assignment does not count as a test

Answers

Answer:

Given:

[tex]\begin{gathered} \sin \alpha=\frac{40}{41}first\text{ quadrant} \\ \sin \beta=\frac{4}{5},\sec ondquadrant \end{gathered}[/tex]

Step 1:

Figure out the value of cos alpha

We will use the Pythagoras theorem below

[tex]\begin{gathered} \text{hyp}^2=\text{opp}^2+\text{adj}^2 \\ \text{hyp}=41,\text{opp}=40,\text{adj}=x \\ 41^2=40^2+x^2 \\ 1681=1600+x^2 \\ x^2=1681-1600 \\ x^2=81 \\ x=\sqrt[]{81} \\ x=9 \end{gathered}[/tex]

Hence,

[tex]\begin{gathered} \cos \alpha=\frac{\text{adjacent}}{\text{hypotenus}} \\ \cos \alpha=\frac{9}{41} \end{gathered}[/tex]

Step 2:

Figure out the value of cos beta

To figure this out, we will use the Pythagoras theorem below

[tex]\begin{gathered} \text{hyp}^2=\text{opp}^2+\text{adj}^2 \\ \text{hyp}=5,\text{opp}=4,\text{adj}=y \\ 5^2=4^2+y^2 \\ 25=16+y^2 \\ y^2=25-16 \\ y^2=9 \\ y=\sqrt[]{9} \\ y=3 \end{gathered}[/tex]

Hence,

[tex]\begin{gathered} \cos \beta=\frac{\text{adjacent}}{\text{hypotenus}} \\ \cos \beta=-\frac{3}{5}(\cos \text{ is negative on the second quadrant)} \end{gathered}[/tex]

Step 3:

[tex]\cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta[/tex]

By substituting the values, we will have

[tex]\begin{gathered} \cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta \\ \cos (\alpha+\beta)=\frac{9}{41}\times-\frac{3}{5}-\frac{40}{41}\times\frac{4}{5} \\ \cos (\alpha+\beta)=-\frac{27}{205}-\frac{160}{205} \\ \cos (\alpha+\beta)=-\frac{187}{205} \end{gathered}[/tex]

Hence,

The final answer = -187/205

Can u help me with my math I’m confused and don’t know

Answers

We want to find the area of the rectangle.

The area of a rectangle is given by;

[tex]\text{Area}=\text{Length x Breadth}[/tex]

The length is x + 7 and the breadth is given by x + 5.

Thus the area is;

[tex]\begin{gathered} A=(x+7)(x+5) \\ A=x^2+7x+5x+35 \\ A=x^2+12x+35 \end{gathered}[/tex]

Therefore, the area is;

[tex]A=x^2+12x+35[/tex]

A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43

Answers

Their total dinner bill including sales tax rate is 8% and  18% tip will be  $156.43 by using the concept of percentages and addition.

What is percent?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

What is sales tax?

A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.

Here,

$122.75 dollars to be paid without tax and tip,

=8% of $122.75

=$9.82.

=122.75+9.82

=$132.57

=18% of 132.57

=$23.86

=132.57+23.86

=$156.43

Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.

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A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces, and is carefully consideringwhich song to play first, second, etc. to create a good flow. How many different recital programs arepossible?

Answers

Given 25 pieces of repertoire, if a pianist plans to play 4 pieces at a recital and is considering playing which song to play first, second, etc, the possible ways is,

[tex]^{25}P_4=\frac{25!}{(25-4)!}=\frac{25!}{21!}=303600\text{ possible recital programs}[/tex]

Hence, the different recital programs possible is 303600

how many inches are in 20 centimeters?

Answers

We know that an inch is equivalent to 2.54 centimeters, then if we want to know how many inches are in a centimeters we do this:

[tex]a\times\frac{1inch}{2.54\operatorname{cm}}[/tex]

In this case, we have 20 centimeters, then replacing a by 20 we find the equivalent inches to 20 like this:

[tex]20\text{cm}\times\frac{1inch}{2.54\operatorname{cm}}\approx7.87\text{inches}[/tex]

In Mrs. Franco‘s class for every 64 is there a April right the ratio of boys to girls in simplest form

Answers

The ratio of boys to girls in Mrs. Franco's class is 3:2 .

The Ratio is defined as the comparison of two quantities that have the same units .

In the question ,

it is given that

In Mrs. Franco's class

For every 6 boys there are 4 girls in the class

we have to find the ratio of , boys to girls

the number of boys = 6

the number of girls = 4

So , the ratio can be written as

boys / girls = 6/4

writing the ratio in the simplest form , we get

boys/girls = 3/2

the ratio is 3:2   .

Therefore , The ratio of boys to girls in Mrs. Franco's class is 3:2 .

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i need help with this question

Answers

Answer:

8%.

Step-by-step explanation:

The perimeter = 2(20 + 30)

                         = 100 cm.

The new perimeter = 2(20 + 0.05*20 + 30 + 30*0.10)

                                 = 2(21 + 33)

                                 = 2*54

                                 = 108 cm.

Percent increases = 8%.

Simplify the numerical expression (3^2 * 5^-1)^2

Answers

Simplify the numerical expression

[tex](3^2\cdot5^{-1})^{2}[/tex][tex]\begin{gathered} (9\cdot\frac{1}{5})^{2}= \\ (\frac{9}{5})^{2}= \\ \frac{81}{25} \end{gathered}[/tex]

I would like to know the answer to -y+9x=0

Answers

Given

-y+9x=0

Find

check if equation model direct variation

Explanation

Equations with direct variation has a general form of y=kx

Given Equation

-y+9x=0

y=9x

whick is in the form of y=kx

Hence this equation is in direct variation with k=9

Final Answer

This equation is in direct variation with k=9

can someone please help!!!

Answers

The simplified expression is as follows:

[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]

How to simplify expression?

The expression can be simplified as follows:

To simplify an expression means to write an equivalent expression which contains no similar terms.

This means that we will rewrite the expression with the fewest terms possible.

Therefore,

[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } }[/tex]

The expression can be represented as follows:

3x⁶ / 14y⁹ ÷ 33x⁴ / 10y²

3x⁶ / 14y⁹ × 10y² / 33x⁴

Hence,

3x⁶ / 14y⁹ × 10y² / 33x⁴  = 30x⁶y² / 462x⁴y⁹

Therefore,

30x⁶y² / 462x⁴y⁹ = 10x² / 154y⁷ = 5x² / 77y⁷

Hence,

[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]

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can you please solve this for me I'll make sure to give the best review

Answers

-9 is an integer

the location of -9 is with 41

6.3 is a repeating decimal

the location is with 5.86666...

-4/5 is a fraction

the location is with 11/12

6. sin D - Ог F 25 ot E 7. cos F. 24 8. sin F Nodule 13

Answers

In the given triangle :

FD = 25, FE = 7, DE = 24

SinD

From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,

So, the SinD is express as :

[tex]\begin{gathered} \sin D=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin D=\frac{FE}{DF} \\ \sin D=\frac{7}{25} \end{gathered}[/tex]

sin D = 7/25

cos F

From the trignometric ratio of cos : It expresses as the ratio of measurement of the side adjacent to the angle and to the hypotenuse of the triangle

So, the Cos F is express as :

[tex]\begin{gathered} \cos F=\frac{Adjacent\text{ side}}{Hypotenuse} \\ \cos F=\frac{FE}{DF} \\ \cos F=\frac{7}{25} \end{gathered}[/tex]

cos F = 7/25

Sin F

From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,

so, Sin F is express as :

[tex]\begin{gathered} \sin F=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin F=\frac{DE}{DF} \\ \sin F=\frac{24}{25} \end{gathered}[/tex]

sin F = 24/25

Answer :

sin D = 7/25

cos F = 7/25

sin F = 24/25

As a town gets smaller, the population of its high school decreases 6% each year. The senior class has 320 students now. In how many years will the high school have 100 students?

Answers

From the details provided, we know that the population of the town gets smaller, that is, a decline and not a growth. The annual rate of decline (or decay) is 6% (or 0.06). The formula for this is given as shown below;

[tex]y=a(1-r)^x_{}[/tex]

The variables here are;

[tex]\begin{gathered} a=\text{initial value} \\ r=\text{rate of decline} \\ x=\text{period (in years)} \end{gathered}[/tex]

The equation to represent the decline of this town's student population shall be;

[tex]\begin{gathered} y=320(1-0.06)^n \\ Simplified,\text{ we now have;} \\ y=320(0.94)^n \end{gathered}[/tex]

When the population ofnthe town becomes 100, then we can replace variable y with 100. Since the formula is used to find the current population, and we have been given the population after a certain number of years, then our y is now 100.

We can now determine the number of years (variable n) that it takes before the population declines to 100 as shown below;

then our y is now 100.

We can now

Using trigonometry functions find the value missing in the diagram round to the nearest whole number

Answers

Given a right angle triangle

As shown:

Given ∠58

the opposite side to the angle = 22

The adjacent side to the angle = x

So,

[tex]\begin{gathered} \tan 58=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 58=\frac{22}{x} \end{gathered}[/tex]

solve for x:

[tex]x=\frac{22}{\tan 58}\approx13.747[/tex]

round to the nearest whole number

So, the answer will be x = 14

Hoang has worked as a nurse at Springfield General Hospital for 6 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?

Answers

Ok let's take the information given and make an equations system with it.

I'm gonna use H for Hoang present working years and B for those of Bill. We know that right now Hoang has worked for 6 years longer than Bill, with this we can create the following equation:

[tex]H=B+6[/tex]

We also have information from two years ago, at that time Hoang's working years doubled Bill's working years. One would feel tempted to write the equation H=2*B but you have to remember that this information is from the past and H and B stand for working years in the present. The correct way to approach this is change H and B by H-2 and B-2 so we consider that this information is from 2 years ago:

[tex]\begin{gathered} (H-2)=2\cdot(B-2) \\ H-2=2B-4 \\ H-2B=-2 \end{gathered}[/tex]

So now we have constructed our equations system:

[tex]\begin{gathered} H=B+6 \\ H-2B=-2 \end{gathered}[/tex]

Let's take the outcome of the first equation and use it in the second one:

[tex]\begin{gathered} H-2B=(B+6)-2B=-2 \\ B-2B+6=-2 \\ -B=-2-6=-8 \\ B=8 \end{gathered}[/tex]

And going back to the first equation:

[tex]H=8+6=14[/tex]

So Hoang has been working at the hospital for 14 years and Bill for 8 years.

Write the standard form of the equation of the circle described below

Answers

Given:

Center ( 8, -4)

Radius (r) = 3

Find-:

Standard equation of a circle

Explanation-:

The standard equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where,

[tex]\begin{gathered} (h,k)=\text{ Center} \\ \\ r=\text{ Radius} \end{gathered}[/tex]

So equation of circle is:

[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (h,k)=(8,-4) \\ \\ r=3 \end{gathered}[/tex][tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ (x-8)^2+(y-(-4))^2=3^2 \\ \\ (x-8)^2+(y+4)^2=9 \end{gathered}[/tex]

4. You are making guacamole for a familygathering. Your first trip to the store, youpurchased 5 avocados and 3 pounds of tomatoesfor $13.30. The head count changed, and youwent back for an additional 3 avocados and 8pounds of tomatoes, spending another $22.55.What is the price per avocado and pound oftomatoes?

Answers

hello

to solve this question, we need to write an equation expressing the word problem and solve for the price of each item.

let x represent the cost of avocados

let y represent the cost of tomatoes

[tex]\begin{gathered} 5x+3y=13.30\ldots\text{.equation 1} \\ 3x+8y=22.55\ldots\text{.equation 2} \end{gathered}[/tex]

from equation 1, let's make xthe subject of formula

[tex]\begin{gathered} 5x+3y=13.30 \\ 5x=13.30-3y \\ \text{divide both sides by 5 to solve for x} \\ x=\frac{13.30-3y}{5} \\ \text{this is equation 3} \end{gathered}[/tex]

put equation 3 into equation 2

[tex]\begin{gathered} 3x+8y=22.55 \\ 3(\frac{13.30-3y}{5})+8y=22.55 \\ \frac{39.9-9y}{5}+8y=22.55 \\ \text{solve for y} \\ \frac{39.9-9y+40y}{5}=22.55 \\ \frac{39.9+31y}{5}=22.55 \\ 39.9+31y=22.55\times5 \\ 39.9+31y=112.75 \\ 31y=112.75-39.9 \\ 31y=72.85 \\ y=\frac{72.85}{31} \\ y=2.35 \end{gathered}[/tex]

since y = 2.35, let's put that in either equation 1 or 2

from equation 2

3x + 8y = 22.55

put y = 2.35 and solve for x

[tex]\begin{gathered} 3x+8y=22.55 \\ y=2.35 \\ 3x+8(2.35)=22.55 \\ 3x+18.8=22.55 \\ 3x=22.55-18.8 \\ 3x=3.75 \\ x=\frac{3.75}{3} \\ x=1.25 \end{gathered}[/tex]

from the calculations above, the price per avocado and pound of tomatoes are $1.25 and $2.35 respectively

Please helpMe if your good with mathI appreciate it thank u!

Answers

Let x be the number of tshirt sold.

A/q,

[tex]\begin{gathered} 5x+40=125 \\ \Rightarrow5x=85 \\ \Rightarrow x=17 \end{gathered}[/tex]

Thus the number of tshirt sold is 17.

hi i need help here please help me i am in need of the helps

Answers

The area of the octagon shaped stop sign = areas of the 4 rectangles + 4 triangles + square = 478 in.².

How to Find the Area of a Triangle and the Area of a Rectangle?Area of rectangle = (length)(width).Area of triangle = 1/2(base)(height).Area of square = (side length)².

If the octagon can be decomposed into 4 identical triangles, 4 identical rectangles, and a square, the following are the dimensions of each of the shapes given:

Height of the triangle = (24 - 10)/2 = 7 in.

Base of the triangle = 7 in.

Side length of the square = 10 in.

Length of rectangle = 10 in.

Width of rectangle = 7 in.

The area of the octagon shaped stop sign = 4(1/2 × base × height) + 4(length × width) + (side length)²

Substitute the values into the equation

The area of the octagon shaped stop sign = 4(1/2 × 7 × 7) + 4(10 × 7) + (10)²

The area of the octagon shaped stop sign = 478 in.².

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I can't find the coordinates of midpoint D , must simplify

Answers

We have to find the midpoint coordinates (D) of segment AB.

We can calculate the coordinates of the midpoint as:

[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2}=\frac{-6x+(-2x)}{2}=\frac{-8x}{2}=-4x \\ \\ y_M=\frac{y_A+y_B}{2}=\frac{4y+(-4y)}{2}=\frac{4y-4y}{2}=0 \end{gathered}[/tex]

Answer: D = (-4x, 0)

In 2000, the population of a town was 46.020. By 2002 wpulation had increased to52,070. Assuming that the towns population is increasing linearly answer the followingquestions.a.What is the population of the town by 2006?

Answers

We know that the population increased linearly, so an adequate model for the population P in year t is:

[tex]P(t)=m\cdot t+b[/tex]

We know that in 2000 the population is 46,020.

In 2002 the population is 52,070.

This are two points of the line that can be written as (2000, 46020) and (2002, 52070).

Then, we can calculate the slope m as:

[tex]m=\frac{P_2-P_1}{t_2-t_1}=\frac{52070-46020}{2002-2000}=\frac{6050}{2}=3025[/tex]

With the slope value we can write the equation in slope-point form:

[tex]\begin{gathered} P-P_0=m(t-t_0) \\ P-46020=3025(t-2000) \\ P=3025(t-2000)+46020 \end{gathered}[/tex]

With the linear equation defined like this (we don't need to calculate the y-intercept), we can calculate the population expected for 2006:

[tex]\begin{gathered} P(2006)=3025(2006-2000)+46020 \\ P(2006)=3025\cdot6+46020 \\ P(2006)=18150+46020 \\ P(20060)=64170 \end{gathered}[/tex]

Answer: the population in 2006 is expected to be 64,170.

Can the three segments below form a triangle? Explain how you will change the length of one or two of these segments to form each kind of triangle. If no changes needed enter the original length or state that no changes needed. scalene triangleAB=… BC=…. AC=… equilateral triangleAB = … BC = … AC = …isosceles triangleAB = … BC = … AC = …

Answers

ANSWERS

• They cannot form a triangle

,

• Scalene triangle: ,AB = 7

,

• Equilateral triangle: ,BC = 5, AC = 5

,

• Isosceles triangle: ,AB = 8

EXPLANATION

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side,

[tex]\begin{gathered} 14+8>5\Rightarrow true \\ 14+5>8\Rightarrow true \\ 5+8>14\Rightarrow false \end{gathered}[/tex]

Hence, these side lengths cannot form a triangle.

To form a scalene triangle one of the shortest sides must be larger, for example, AB should be 7, instead of 5. Other combinations are possible as well.

To form an equilateral triangle all sides must have the same length, for example, AB = BC = AC = 5

To form an isosceles triangle, two of the sides must have the same length, while the third side has a different length, for example, AB = 8

To form all three kinds of triangles, the first rule must be valid as well.

Rewrite the function by completing the square. f (x)= x^2 - 9x + 14

f (x) = _ ( x + _ )^2 + _

Answers

Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

f(x) = x² - 9x + 14x² - 9x + 14 = 0x² - 9x = -14

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

-9-4.520.25

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

x² - 9x + 20.25 = -14 + 20.25(x - 4.5)² = 6.25(x - 4.5)²- 6.25 = 0

Convert this back to function form:

f(x) = 1(x - 4.5)² - 6.25

The equation is f(x) = 1(x - 4.5)² - 6.25.

A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 9 years? Round your answer to the nearest dollar.

Answers

Given:

[tex]\begin{gathered} \text{Principal(P)}=\text{ \$3100 } \\ r=5.5\text{ \%} \\ n=9 \end{gathered}[/tex][tex]Final\text{ amount=P(1+}\frac{r}{100})^n[/tex][tex]\begin{gathered} Final\text{ amount after 9 years=}3100(1+\frac{5.5}{100})^9 \\ =3100(1.6191) \\ =\text{ \$50}19.21 \end{gathered}[/tex]

Therefore, the investment be worth after 9 years is $5019.21

The table shows the earnings and the number of hours worked for five employees. complete the table by finding the missing values.

Answers

The first employee

[tex]\begin{gathered} He\text{ earns a total of \$12.75} \\ \text{His working rate is \$}8.50\text{ per hour} \\ \text{Hours he workd can be calculated below} \\ \text{ \$8.50 = 1 hour} \\ \text{ \$12.75 =?} \\ \text{ number of hours=}\frac{12.75}{8.50} \\ \text{ number of hours = 1.5 hours} \end{gathered}[/tex]

The second employee

[tex]\text{ earning per hour = }\frac{19.09}{2.3}=\text{ \$8.3 per hour}[/tex]

The third employee

[tex]\begin{gathered} \text{ \$7.75=1 hour} \\ \text{ \$26.}35=\text{?} \\ \text{ number of hours=}\frac{26.35}{7.75}=3.4\text{ hours} \end{gathered}[/tex]

The fourth employee

[tex]\text{earning per hour = }\frac{49.50}{4.5}=\text{ \$}11\text{ per hour}[/tex]

The fifth employee

[tex]\text{earning per hour=}\frac{31.50}{1.5}=\text{ \$21 per hour}[/tex]

Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes.SportsPlus, a rival shoe manufacturer, then came up with a design that it claims performs even better than Fastex's design. A sports magazinedecided to test the claims. It created two groups of 15 randomly selected athletes each. Members of both groups were pretested anddetermined to have equal athletic ability. Additionally, they followed the same nutrition plan and training program during the study.The athletes did a 1-mile run to test the shoes. The magazine found that the athletes who used Fastex shoes had reduced their 1-mile run timeby an average of 396, and athletes who used Sports Plus shoes had reduced their 1-mile run time by an average of 2%.Given the magazine's data collection method and findings, what conclusion can be made?OA. The data collection method used was fair since both shoe designs were tested on identical parameters.OB. The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.OC. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than theathletes given SportsPlus shoes.OD. The data collection method used was random since the athletes in the two groups used two different shoe designs.

Answers

B: The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.

This is false because they followed the same nutrition plan and training program during the study.

C. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes.

This is also false because members of both groups were pretested and determined to have equal athletic ability

D. Each group used one shoe design.

So, the correct option is A

which answer choice gives the correct surface area for a triangular prism with bases that are 4 cm2 and sides that are 10 cm2? A. 12 cm2 B. 26 cm2 C.38 cm2 D. 40 cm2

Answers

Explanation

A trinagular prism has two bass and theree side surfaces.

Therefore, the suface area pf the prism is

[tex]S.A=3(10)+2(4)=30+8=38cm^2[/tex]

Answer: Option C

Find the oth term of the geometric sequence 5,--25, 125,

Answers

Given the geometric progression below

[tex]5,-25,125,\ldots[/tex]

The nth term of a geometric progression is given below

[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]

From the geometric progression, we can deduce the following

[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]

To find the value of r, we will take ratios of two consecutive terms

[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]

To find the 9th term of the geometric, we will have that;

[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]

Hence, the 9th term of the geometric progression is 1953125


Please help me step by step

Answers

The value of the function f(x) at x = 0 is found as -1.

What is meant by the term function?A function is described as the connection between such a set of inputs that each have one output. A function is a relationship between inputs in which each input is linked to exactly one output. Every function does have a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x would be the input. A function's general representation is y = f(x). In mathematics, a function is a special relationship between inputs (the domain) and outputs (the codomain), where each input has precisely one output and the output could be traced all the way back to its input.

For the given question,

The graph of the function f(x) = -x² + 4x - 1 is given.

For finding the value of f(x) at x = 0, check the y-coordinate of the graph when x = 0.

Put x = 0 in the given function.

f(0) = -0² + 40 - 1

f(0) = - 1

Thus, the value of the function f(x) at x = 0 is found as -1.

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