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If a scale factor of One-fifth is used to make a reduction, what is the base of the original triangle?

Answer:

  y = -1/8(x -1)² +4

Step-by-step explanation:

The equation of a parabola can be written from focus and directrix using the form ...

  y = 1/(4p)(x -h)² +k

where p is the distance from vertex to focus, and (h, k) is the vertex.

The vertex-focus distance is half the distance from the directrix to the focus. Here, that is ...

  p = (2 -6)/2 = -4/2 = -2

The vertex is halfway between the focus and directrix on the same vertical line, so has coordinates ...

  (h, k) = ((1, 2) +(1, 6))/2 = (1, 4)

__

Using these values of p and (h, k), we find the equation of the parabola to be ...

  y = 1/(4(-2))(x -1)² +4

  y = -1/8(x -1)² +4

_____

Additional comment

You can check the graph by considering the definition of a parabola: each point on the curve is equidistant from the focus and the directrix. This is easily verified for points on the horizontal and vertical lines through the focus. For example, point (5, 2) is 4 units from the focus, and 4 units from the directrix.

Answer:

y=-1/8(x-1)^2 +4

Step-by-step explanation:

Answer:

A mango costs $4.68, a coke costs $1.56 and a taco costs $4.25

Step-by-step explanation:

Given

Represent Tacos with T, Coke with C and Mango with M

For Grace:

[tex]2T + C + M = 14.74[/tex] --- (1)

For Mia:

[tex]5T + 2C + M = 29.05[/tex] -- (2)

[tex]M = 3C[/tex]

Required

Determine the cost of each item

Substitute 3C for M in (1) & (2)

[tex]2T + C + M = 14.74[/tex]

[tex]2T + C + 3C = 14.74[/tex]

[tex]2T + 4C = 14.74[/tex] --- (4)

[tex]5T + 2C + M = 29.05[/tex]

[tex]5T + 2C + 3C = 29.05[/tex]

[tex]5T + 5C = 29.05[/tex] --- (5)

Divide through (5) by 5

[tex]T + C = 5.81[/tex]

Solve for C

[tex]C= 5.81 - T[/tex]

Substitute 5.81 - T for C in (4)

[tex]2T + 4C = 14.74[/tex]

[tex]2T + 4(5.81 - T) = 14.74[/tex]

[tex]2T + 23.24 - 4T = 14.74[/tex]

Collect Like Terms

[tex]2T - 4T = 14.74 - 23.24[/tex]

[tex]-2T= -8.5[/tex]

Solve for T

[tex]T = -8.5/-2[/tex]

[tex]T = 4.25[/tex]

Recall that:

[tex]C= 5.81 - T[/tex]

[tex]C = 5.81 - 4.25[/tex]

[tex]C = 1.56[/tex]

Recall that

[tex]M = 3C[/tex]

[tex]M = 3 * 1.56[/tex]

[tex]M = 4.68[/tex]

Hence:

A mango costs $4.68, a coke costs $1.56 and a taco costs $4.25

Answer: Inverse

Explanation: Any conditions that doesn't fit the requirement of the conditional statement would make the statement false, therefore it is inverse.

Answer:   7:3 is the ratio of the problem

Step-by-step explanation:

Answer:

f(2) = [tex]\frac{25}{8}[/tex]

Step-by-step explanation:

To evaluate f(2) substitute x = 2 into f(x) , that is

f(2) = [tex]\frac{1}{8}[/tex] × 5² = [tex]\frac{1}{8}[/tex] × 25 = [tex]\frac{25}{8}[/tex]

Answer:

24/8

Step-by-step explanation:

BIG BRAIN

Answer:

-17/24

Step-by-step explanation:

Because they are negative numbers, the smaller fraction (when disregarding the negative sign) is always a larger number. -11/12 could be changed to -22/24, and therefore since it is a larger number when disregarding the negative (22/24), it is a smaller number altogether.

-17/24 > -22/24

Answer:

$85,000

Step-by-step explanation:

Given that, the annual salary of the governor of New York was $179,000.

Let $y be the annual salary of the governor of Tennesse during the same year.

As the annual salary of the governor of Tennessee was $94,000 less than the annual salary of the governor of New York.

So, the annual salary of the governor of Tennesse,

[tex]y=179000-94000[/tex]

[tex]\Rightarrow y=85000[/tex]

Hence, the annual salary of the governor of Tennesse during the same year was $85,000.

Answer:

D

Step-by-step explanation:

sorry about last time 100% sure about this one

Answer: D, because y =mx + b

Answer:

The coordinates of its image are (2, -4)

Step-by-step explanation:

Let us revise the rules of reflection across the axes

∵ The point (2, 4) is reflected across the x-axis

→ By using the first rule above rx-axis (x, y) → (x, -y)

∴ Change the sign of its y-coordinate

∴ Its image is (2, -4)

∴ The coordinates of its image are (2, -4)

Answer:

3(x + 8y)

Step-by-step explanation:

3 is the highest term that can be factored out; there are no other numbers/variables in common.

Factor out 3 from 3x + 24y.

= 3(x+8y)

The factored form of the given expression is 3(x+8y).

A factor is a number that divides into another number without a remainder. So, for example, 5 is a factor of 20 because 20/5 = 4. There is no remainder. You can also think of factors as the numbers that you multiply together in order to obtain a product.

Given is an expression 3x+24y, we need to find the factors of the given expression,

3x+24y

Since, 3 is the highest term that can be factored out; there are no other numbers/variables in common.

Factor out 3 from 3x + 24y.

= 3(x+8y)

Hence, the factored form of the given expression is 3(x+8y).

Learn more about factors, click;

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Answer:

3 eggs

Step-by-step explanation:

For 12 cupcakes, 2eggs are required.

For 18 cupcakes, 3 eggs are required.

[Use multiplication table of 6, 6*2=12 and 6*3=18]

Answer:

21 pencils for Nick and 63 pencils for Lance

Step-by-step explanation:

Now let's make an equation out of the information above:

3x + x = 84

Now solve for x.

3x + x = 84

4x = 84

x = 84/4

x = 21

So Nick has 21 pencils

Now for Lance:

3x

3 * (21) = 63

So Lance has 63 pencils

63 + 21 = 84 pencils

Answer:

0

Step-by-step explanation:

63/7 = 9

We know,

If any number smaller then fifty told to be rounded to its nearest hundred then the answer is ' 0 '

Similarly the nearest hundred of 9 is 0.

Hope it helps

Mark me brainliest.

= 10 (u + 9)

= 10 x u + 10 x 9

= 10u + 90

Answer:

Yes

Step-by-step explanation:

It helps you to understand the equation easily

HOPE IT HELPED

Answer:

1 ft³ of gold will weigh 1209.6 pounds

1 ft³ of copper will weigh 559 pounds.

Step-by-step explanation:

We know the formula for:

Density = Mass/Volume

Hence, making mass the subject of the formula:

Mass = Density × Volume

From the question we are told:Volume of each metal = 1 ft³

1) Metal: Gold

Density of Gold = 0.70 pounds per cubic inch(lb/in³)

We convert the Volume of gold from ft³ to in³

The Volume of gold given in the question = 1 cubic foot = 1 ft³

1 cubic foot = 1728 cubic inches

Hence, the volume of Gold = 1728 in³

Mass of Gold = Density of Gold × Volume of Gold

Mass of Gold = 0.70Ib/in³ × 1728 in³

= 1209.6 lb(pounds)

2) Metal : Copper

Density of copper given in the question = 8.96 grams per cubic centimeter

Ib = pounds

We convert this density in g/cm³ to ib/in³

453.5g = 1 Ib

8.96g = a Ib

Cross Multiply

= 453.5g × a Ib =8.96g × 1 Ib

= a Ib = 8.96g × 1 Ib/453.5g

a Ib = 0.0197574421 Ib

Density of Copper = 0.0197574421 Ib/cm³

28,316.8 cm³ = 1 ft³

1 cm³ = b ft³

b ft³ = 1 cm³ × 1 ft³/28,316.8cm³

b ft³ = 0.0000353147 ft³

1 cm³ = 0.0000353147 ft³

We have to convert the density of Copper from Ib/cm³ to Ib/ft³

0.0197574421 Ib/cm³ = 0.0197574421 Ib/0.0000353147 ft³

559.46793026 Ib/ft³

Volume of copper = 1ft³

Mass = Density × Volume

Mass of copper = 559.46793026 Ib/ft³ × 1 ft³

= 559.46793026 Ib or pounds

≈ 559 pounds

Therefore , the weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.

Answer:

Gold

Density of Gold = 0.70 pounds per cubic inch

1 cubic foot = 1728 cubic inches

Hence, the volume of Gold = 1728 in³

Mass of Gold = Density of Gold × Volume of Gold

Mass of Gold = 0.70Ib/in³ × 1728 in³ = 1209.6 lb(pounds)

2) Metal : Copper

Density of copper given in the question = 8.96 grams per cubic centimeter

We convert this density in g/cm³ to ib/in³

453.5g × a Ib =8.96g × 1 Ib = 8.96g × 1 Ib/453.5g = 0.0197574421 Ib

Density of Copper = 0.0197574421 Ib/cm³

Volume of copper = 1ft³

Mass = Density × Volume

Mass of copper = 559.46793026 Ib/ft³ × 1 ft³ = 559.46793026 Ib or pounds

≈ 559 pounds

The weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.

Answer:

A small slushee has 12 ounces.

A medium 29 ounces.

And a large 72 ounces.

Step-by-step explanation:

Let s represent the size of the small slushee, m the medium slushee, and l the large slushee.

We know that the medium slushee has 17 more ounces than the small slushee. So:

[tex]m=s+17[/tex]

We also know that the large slushee l has 6 times as many ounces than the small slushee. Therefore:

[tex]l=6s[/tex]

Finally, we know that there are a total of 113 ounces in the small, medium, and large drinks combined. So:

[tex]s+m+l=113[/tex]

We can solve this triple system of equations using substitution. Let's substitute l for 6s and m for (s+17). This yields:

[tex]s+(s+17)+(6s)=113[/tex]

Combine like terms:

[tex]8s+17=113[/tex]

Subtract 17 from both sides:

[tex]8s=96[/tex]

Divide both sides by 8:

[tex]s=12\text{ oz}[/tex]

So, the small slushee is 12 ounces.

So, the medium slushee is [tex]12+17=29\text{ oz}[/tex]

And the large slushee is [tex]6(12)=72\text{ oz}[/tex]

And we're done!

Answer:

square the vertical starting from bisect angle !

Answer:

3xy-15 thats the simplified form

5/2 can be written as 2 1/2

2*2 = 4 + 1 = 5

Answer:

2 1/2

Step-by-step explanation:

you divide 5 into 2, to get 2 and 1 left over

Answer:

5.8

Step-by-step explanation:

[tex]\sqrt{5^{2} + (-3)^{2} } \\\sqrt{25 + 9} \\\sqrt{34}[/tex]

5.83

hope it helps

Answer:

5.8

Step-by-step explanation:

well, you use the distance formula to find the magnitude of this vector.

Hope this helps!

Answer: i think 130 and 80

Step-by-step explanation: sorry if wrong

Answer:

the answer is b because that's the slope

Answer:

B

Step-by-step explanation:

you can try each answer or you can just use number of plants and divide it by number of seed packets which is 10 so B

Answer:

175[tex]mm^{2}[/tex]

Step-by-step explanation:

Just divide the larger one by 7 because the scaled one is 1/7 the size of the larger one:

1225 ÷ 7 = 175

Pls consider giving me Brainliest! It would mean and help a lot! ; )

Answer:

175

Step-by-step explanation:

Answer:

Step-by-step explanation: Your adding 2. So 1 + 2= 3, 3 + 4 =7, 7 + 8=15, 15 + 16=31. You see my point. My wording is off.

Answer:

72.45°

Step-by-step explanation:

Add 7.65° to 64.8°

The temperature is 72.45° on Tuesday.

Hope I helped :)

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Answer:

Step-by-step explanation:

Monday=64.8

Tuesday= 64.8+7.65

=72.45