A flagpole casts a 16-foot shadow at the same time a 4-foot pole casts a 5-foot shadow. How tall is the flagpole?

graph A

no x-intercept

no y-intercept

H.A is y = 5

V. A. is x = 0

*****************************************

Answer: [tex]\frac{150}{31}[/tex]

Step by step explanation:

log₆(5x + 6) - log₆(x - 4) = 2

log₆[tex](\frac{5x+6}{x-4})[/tex] = 2

[tex](\frac{5x+6}{x-4})[/tex] = 6²

[tex](\frac{5x+6}{x-4})[/tex] = 36

5x + 6 = 36(x - 4)

5x + 6 = 36x - 144

       6 = 31x - 144

    150 = 31x

     [tex]\frac{150}{31}[/tex] = x

**********************************************************

Answers:

Explanation:

f(x) = 3x² + 6x - 2

      a=3  b=6 c=-2

x = [tex]\frac{-b}{2a} =\frac{-6}{2(3)} = \frac{-6}{6} = -1[/tex]

Axis Of Symmetry: x = -1

f(-1) = 3(-1)² + 6(-1) - 2

       = 3 - 6 - 2

       = -5

Vertex: (-1, -5)

x = [tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex]

  = [tex]\frac{-6+/-\sqrt{6^{2}-4(3)(-2)}}{2(3)}[/tex]

  = [tex]\frac{-6+/-\sqrt{36+24}}{6}[/tex]

  = [tex]\frac{-6+/-\sqrt{60}}{6}[/tex]

  = [tex]\frac{-6+/-2\sqrt{15}}{6}[/tex]

  = [tex]\frac{-2+/-\sqrt{15}}{3}[/tex]

x-intercepts: [tex]\frac{-2+/-\sqrt{15}}{3}[/tex]

Answer:

Side DF = 4 units

Step-by-step explanation:

Similar triangles states that the triangles with equal corresponding angles and proportionate sides.

Given: ΔABC and ΔDEF are similar

Corresponding angles are;

[tex]\angle A = \angle D[/tex] ,  

[tex]\angle B = \angle C[/tex] ,

[tex]\angle C= \angle F[/tex]

Proportionate sides are;

[tex]\frac{AB}{DE} =\frac{BC}{EF} =\frac{AC}{DF}[/tex]

It is also given BC = 6 units , EF = 8 units and DF -AC = 1

Let AC = x units then;

DF = x +1 units.

Then, by definition of similar triangle ;

[tex]\frac{BC}{EF} =\frac{AC}{DF}[/tex]

[tex]\frac{6}{8} =\frac{x}{x+1}[/tex]

By cross multiply we have;

[tex]6(x+1) = 8x[/tex]

Using distributive property;  [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]

6x + 6 = 8x

Subtract 6x on both sides we get;

6x + 6 -6x = 8x -6x

Simplify:

6 = 2x

Divide by 2 on both sides we get;

x = 3

DF = x +1  = 3+1 = 4

Therefore, the side DF is, 4 units

Answer:

D) Only (-1,9) is a solution.

Step-by-step explanation:

x+y =8

x^2 + y = 10

Lets check the first point (-1,9)

Put in x =-1 y =9

x+y =8

-1+9 = 8

8 =8

This works

x^2 + y = 10

(-1)^2 +9 =10

1+9 = 10

10 = 10

This works

Lets check the second point (-2,6)

Put in x =-2 y =6

x+y =8

-2+6 = 8

4=8

This  does not work

We can stop now.  (-2,6) cannot be a solution

After substituting the given pairs into both equations, only the pair (-1,9) satisfies the system of equations, meaning Only (-1,9) is a solution (D).

To determine if the given pairs (-1,9) and (-2,6) are solutions to the system of equations x + y = 8 and x² + y = 10, we need to plug the x and y values from each pair into the equations and check for their validity.

Checking Pair (-1,9):

For the first equation:

For the second equation:

Checking Pair (-2,6):

For the first equation:

For the second equation, the check is unnecessary as the pair already failed the first equation.

Therefore, the correct answer is D) Only (-1,9) is a solution.

Answer:

a. -2, odd; -1, odd; 1, odd; 2, odd

b. [tex](x+2)(x+1)(x-1)(x-2)[/tex]

c. even likely degree 4

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

In this graph, there are four real zeros: -2,-1,1,2

We can write them in intercept or factored form as (x-2), (x-1), (x+1) and (x+2).

Because the graph crosses the x-axis at -2, it's multiplicity is odd likely 1. This is the same for each of the zeros or x-intercepts.

The graph a W shape and facing upwards so it has a positive leading coefficient with an even degree.

This means the function has a degree of 4 or higher with the degree being even.

Final answer:

To find the original price of a pizza before a 20% discount that resulted in a final price of £5.60, divide the final price by 0.8. The original price is calculated to be £7.00.

Explanation:

The question involves determining the original price of a pizza before a 20% discount was applied, given that the reduced price after the discount is £5.60.

To calculate the original price, we can use the formula for finding the original price when the final price and discount rate are known.

Let's denote the original price as OP. Since a 20% discount was applied, the pizza sold for 80% of its original price. The equation representing this situation is:

0.8 × OP = £5.60

Now, we divide the reduced price by 0.8 to find the original price:

OP = £5.60 / 0.8

OP = £7.00

Thus, the original price of the pizza was £7.00 before the 20% discount was applied.

Final answer:

Writing a linear equation requires knowing the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, and the point-slope form (y - y1 = m(x - x1)), useful when a point on the line and the slope are known.

Explanation:

The ability to write a linear equation involves understanding different forms, such as standard form, point-slope form, and slope-intercept form. The slope-intercept form of a linear equation is commonly written as y = mx + b, where m represents the slope and b represents the y-intercept. The slope is the rate of change, indicating how much y increases for a one-unit increase in x. The y-intercept is the point where the line cuts the y-axis, which means when x=0.

It's important to note some variations in notation, such as y = a + bx, which is another way to express the slope-intercept form, where a is the y-intercept and b is the slope. When converting between forms, it's essential to identify these components correctly to maintain the equation's integrity.

In point-slope form, an equation of a line is written as y - y1 = m(x - x1), where (x1, y1) is a known point on the line, and m is the slope. This form is particularly useful when you have a point and a slope and need to write the equation of the line.

Answer:

Natasha charges $30 per house

Step-by-step explanation:

Profit =  -126 + 30x

The cost of the cleaning supplies is 126

and the cost per house is 30

x = the number of houses cleaned.

Answer:

3rd one for lesson: Translations of the Square Root Function

Step-by-step explanation:

It should be a parabola that opens upward and is shifted 2 units downward.

The graph of the quadratic function y = x² - 2 typically looks like.

The graph of the quadratic function y = x² - 2 is a parabola. Specifically, it's a upward-opening parabola because the coefficient of the x² term (which is 1) is positive.

- The vertex of the parabola is at the point (0, -2).

- The parabola opens upward, so it does not intersect or cross the x-axis.

- It reaches its minimum value at the vertex, which is -2.

The graph that represents an upward-opening parabola with a vertex at (0, -2) and does not intersect the x-axis. It should be a parabola that opens upward and is shifted 2 units downward.

Learn more about graph here

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Answer:

8

Step-by-step explanation:

160 divided by 20 hours = 8.

David has a 8 hourly wage.

Your answer would be $8. 20hrs divided into $160=$8

Hope this helps....

Answer: 33 and 28

Step-by-step explanation:

so, all we know is ? + ? = 61

if the larger number is 5 more than the smaller number, we can assume that..

33 + 28 = 61

The mean distance ran by all four of them is 30.

Given is that sum of two numbers is 61 . The larger number is 5 more than the smaller number.

We can write the equations as -

x + y = 61                                               .... Eq{ 1 }

y = x + 5                                                  .... Eq{ 2 }

Now, we can write -

x + y = 61

x + x + 5 = 61

2x = 56

x = 28

and

y = 33

Therefore, the mean distance ran by all four of them is 30.

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Answer:

Height is 18 inches.

Base is 36 inches.

Step-by-step explanation:

Let the base of the triangular table top be x inches.

The height will be [tex]\frac{1}{2}[/tex]x inches.

The area of the triangular table top is 324 inches²

Area of a triangle = [tex]\frac{1}{2}[/tex] × Base × Height

342 inches² = [tex]\frac{1}{2}[/tex] × x × [tex]\frac{1}{2}[/tex]x

[tex]\frac{x^2}{4}[/tex] = 324

Finding the square root on both sides gives;

[tex]\frac{x}{2}[/tex] = 18

Therefore x (the base) = 36 inches

And [tex]\frac{1}{2}[/tex] (the height) = 18 inches.

Final answer:

The height of the triangular table top is 18 inches, and the base is 36 inches, using the formula for the area of a triangle and given that the base is twice the height with an area of 324 square inches.

Explanation:

The question requires finding the height and base of a triangular table top given that the area is 324 square inches and the base is twice as long as the height. To find these dimensions, we can use the formula for the area of a triangle, which is Area (A) = [tex]\frac{1}{2}[/tex] × base (b) × height (h). Given that the base is twice the height, we can express the base as 2h.

Now, we can set up the equation using the given area: 324 = [tex]\frac{1}{2}[/tex] × 2h × h. Simplifying gives us 324 = h², so the height (h) would be the square root of 324, which is 18 inches. The base (2h) is therefore 36 inches. So, the dimensions of the tabletop are a base of 36 inches and a height of 18 inches.

Answer with explanation:

There are two triangles.We will use angle sum property to get the correct Inequality.

In Triangle 1

→x° + a° + 75°=180°

→x° + a°= -75°+180°

→x° + a°= 105°

In triangle 2

→y° + b° + 60°=180°

→y°+b°=180°-60°

→y°+b°=120°

As there are four different variables ,and only two equations.So,we can't determine the value of , a and ,b.

Option D: Can't be Determined

Answers:

Angle A = 62.1 degrees

Angle X corresponds to angle A

The triangles are not similar

=========================================

Explanation:

To find angle A, subtract the given angles B and C from 180 to get 180 - B - C = 180 - 60.8 - 57.1 = 62.1 degrees

Notice how none of the angles of triangle ABC have a measure of 59.1, so this means that angle Y cannot be congruent to any of A, B or C. This is why the triangles are not similar. We would need 2 pairs of congruent angles to use the AA (angle angle) similarity theorem.

If the triangles were similar, then we can say triangle ABC is similar to triangle XYZ. The letters A and X are the first letters mentioned of the trio of letters, which means that they correspond to one another.

Answer:

The total cost of one hot dog, one slice of pizza and one ice cream cone at the county fair is $3.

Step-by-step explanation:

Let us assume that the cost of the one hot dogs be x.

Let us assume that the cost of the one ice cream cone be y.

Let us assume that the cost of the one silce of pizza be z.

As given

At the county fair, two hot dogs and an ice cream cone cost $2.50.

Than the equation becomes

2x + y = 2.50

Two slices of pizza and an ice cream cone cost $3.50.

2z + y = 3.50

Than two equations are

2x + y = 2.50 and 2z + y = 3.50

Adding the both above equation.

2x + y +  2z + y = 2.50 + 3.50

2x + 2z + 2y = 6

[tex]x + y + z = \frac{6}{2}[/tex]

x + y + z = 3

Therefore the total cost of one hot dog, one slice of pizza and one ice cream cone at the county fair is $3.

Answer:

[tex]6^{\frac{1}{5} }=\sqrt[5]{6}[/tex]

[tex]6^{\frac{7}{5} }=\sqrt[5]{6^7}[/tex]

[tex]6^{\frac{1}{6} }=\sqrt[6]{6}[/tex]

[tex]7^{\frac{1}{2} }=\sqrt[2]{7}[/tex]

[tex]7^{\frac{5}{2} }=\sqrt[2]{7^5}[/tex]

[tex]6^{\frac{9}{2} }=\sqrt[2]{6^9}[/tex]

Step-by-step explanation:

A radical is the root operation for n roots such as square root or cuberoot in the form [tex]\sqrt[n]{x}[/tex]. A fraction exponent [tex]x^{m/n}[/tex] can be converted to the radical form.

[tex]6^{\frac{1}{5} }=\sqrt[5]{6}[/tex]

[tex]6^{\frac{7}{5} }=\sqrt[5]{6^7}[/tex]

[tex]6^{\frac{1}{6} }=\sqrt[6]{6}[/tex]

[tex]7^{\frac{1}{2} }=\sqrt[2]{7}[/tex]

[tex]7^{\frac{5}{2} }=\sqrt[2]{7^5}[/tex]

[tex]6^{\frac{9}{2} }=\sqrt[2]{6^9}[/tex]

Answer:

[tex]f(x)=\sqrt[n]{5x}-10[/tex]

Step-by-step explanation:

Parent root function is given by:

[tex]f(x)=\sqrt[n]{x}[/tex]

According to rules,

Combining these 2 transformation gives us the function:

[tex]f(x)=\sqrt[n]{5x} -10[/tex]

Answer choice A is right.

Answer:

A. f(x)= n√5x-10

Answer:

x-intercept = 3 ; y-intercept = -5

Step-by-step explanation:

Lets rearrange the equation into the form y = mx + b:

5x - 3y = 15

-3y = 15 - 5x

Divide by -3:

y = 5x/3 - 5

Here we know that b (-5) is the y-intercept, and we can find the x-intercept by starting at the y-intercept and using the slope till we get the x-intercept. Or you can set y = 0 and solve for x, either way you get x-intercept = 3.

This equation is in standard form, if you put it into slope-intercept form, you will be able to graph it. Once you graph it you will be able to find the intercepts.

5x - 3y = 15

-3y = -5x + 15

y = 5/3x - 5

X-Intercept: (3,0)

Y-Intercept: (0, -5)

Answer:

x=1

Step-by-step explanation:

sqrt(2x-1) =1

We will square both sides

sqrt(2x-1)^2 =1^2

2x-1 =1

Add 1 to each side

2x-1+1 = 1+1

2x=2

Divide by 2

2x/2 =2/2

x=1

Answer:

total cost = $ 81

Step-by-step explanation:

It is given that the fixed cost is $ 39

and the cost per minute is $0.07

Let us assume the number of minutes used be x

we have

total cost = cost per minute × number of minutes used  + fixed cost

we plug the given values, so we have

[tex]total cost = 0.07 x+39[/tex]

we need to find the total cost for 10 hours used

x= 10 hours = 10(60) minutes = 600 minutes

so we have total cost for x= 600 minutes

[tex]total cost = 0.07(600)+39[/tex]

[tex]total cost =42+39 = 81[/tex]

hence the total cost = $ 81

Answer:

a

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Inverse is when you swap the x's and y's and solve for "y":

y = 6x + 1

swap: x = 6y + 1

solve: x - 1 = 6y

      [tex]\dfrac{1}{6}(x-1)=y[/tex]

Answer:

Garden Trees Number

Redbud 2

Magnolia 3

Snowbell 1

Maple 4

Step-by-step explanation:

If the first mark is labeled Redbud and has 2 dots then it has 2 trees.

If the second mark is labeled Mangolia and has 3 dots then it has 3 trees.

If the third mark is labeled Snowbell and has 1 dot then it has 1 tree.

If the fourth mark is labeled Maple and has 4 dots then it has 4 trees.

Answer:

D

Step-by-step explanation:

Answer:

3 adults and 24 students

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 27 tickets were purchased, then s+a=27.

We also know they were purchased for $60 and adult tickets cost $4 and student tickets cost $2. We can write 2s+4a=60.

We will solve by substituting one equation into the other. We start by solving the first equation for c. s+a=27 becomes s=27-a.

Now we substitute s=27-a into 2s+4a=60. Simplify and isolate the variable a.

2s+4a=60

2(27-a)+4a=60

54-2a+4a=60

54+2a=60

54-54+2a=60-54

2a=6

a=3

This means that 3 adults attended and 24 students attended since 3+24=27.

Answer:

Step-by-step explanation:

Any angles on opposite sides of the intersection point of crossing lines are "vertical" angles, and they have identical measure.

Any angles along the same side of the same line are "linear" angles, and they are supplementary (add to 180°).

The angles inside a triangle add to 180°.

Using these relationships, work from the given information to find the rest of the angles.

Answer:

127

Step-by-step explanation:

We can use the Exterior Angle of a Triangle theorem to find x. It states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

We will start with x+5. It is equal to 79 +____ an angle we don't know yet. But we do know that the angle____ and x equals 180 because they form a straight line. Therefore the unknown angle must be 180-x.

So we will set x+5=79+180-x. We will combine like terms, use inverse operations, and isolate.

x+5=79+180-x

x+5=259-x

x+x+5=259-x+x

2x+5=259

2x+5-5=259-5

2x=254

x=127

Answer:

127

Step-by-Step Explanation:

I already did this on edginuety :)

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

Jane mixes 3 pints of blue paint with 4 pints of red paint to get her desired color.

So, the ratio will be

[tex]3:4[/tex]

We have 16 pints of red paint and we have to find the pints of blue paint 'say x'.

According to question,

Since there is "direct variation" . So,our equation becomes,

[tex]\frac{3}{16}=\frac{4}{x}\\\\x=\frac{16\times 4}{3}\\\\x=\frac{64}{3}\\\\x=21.34[/tex]

Hence, Option 'C' is correct.

Answer:

3

4

=  

x

16

given ratio =  

3

4

and,

3

4

=  

12

16

Step-by-step explanation:

The sum does not converge because [tex]\dfrac76>1[/tex].

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

Answer:

The given statement is True

Step-by-step explanation:

WE have to find out that which one has more no of inches

so now we have

100 yards football field

28 meter basketball court

Total no of inches in one yard =  36 inches

Total no of inches in 100 yard = 36 * 100

                                                  = 3600 inches

Now total no of inches in one meter = 39.3701 inches

Total no of inches in 28 meter =  28 * 39.3701

                                                   =1102.3628 inches

So we can see that 1102.3628 is smaller than 3600

So It can also be seen that football field has more inches then a basketball court

So the given statement is True

Answer:

The given statement is true.

Step-by-step explanation:

First we will apply conversions to given terms:

1 yard has = 36 inches

So, 100 yards has = [tex]36\times100=3600[/tex] inches.

1 meter = 100 cm

So, 28 meters has = [tex]28\times100=2800[/tex] cm

So, now upon comparing we can see that 3600 is greater than 2800.

Therefore, the inches in a 100 yard field are greater than the cm in a 28 meter basketball court.

The statement given here is true.

[tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]

An exponent represents repeated multiplication. For example, ...

... x^3 = x·x·x

... x^2 = x·x

If we divide these, the x's in the denominator cancel an equal number in the numerator:

... (x·x·x)/(x·x) = x

If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:

... (x^3)/(x^2) = x^(3-2) = x^1 = x

Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.

Answer:

yes; you can just remember that all the angles on a triangle equal 180 so just add the two angles, subtract from 180 to get your last angle degrees.

Answer:

It took Kaitlyn 13.25 hours to complete the race.

Step-by-step explanation:

1. Take the number of miles and the average speed per mile

2. Multiply the distance by the speed; 11 1/4 x 7 1/2

4. Solve; 13 1/4 hours

5. Convert into decimals; 13.25 hours