Q is between P and R. PR=145,PQ=8x & QR=11x-7. What is the value of QR?

Answer: -7.2

Step-by-step explanation:

The vertex form of quadratic equation :[tex]f (x) = m(x - a)^2 + b,[/tex] where (a,b) is the vertex.

Given: The quadratic function g(x) has a vertex at  (-5, 0).

Put (a,b)= (-5,0) for function g(x), we get

[tex]g(x)=m(x-(-5))^2+0\\\\\Rightarrow\ g(x)=m(x+5)^2[/tex]

Also, its  y-intercept is (0, -5).

Put x= 0 and g(x) =-5

[tex]-5=m(0+5)^2\\\\\Rightarrow\ -5=m(25)\\\\\Rightarrow\ m=\dfrac{-5}{25}\\\\\Rightarrow\ m=\dfrac{-1}{5}[/tex]

so, [tex]g(x)=-\dfrac{1}{5}(x+5)^2[/tex]

For g(1), put x=1

[tex]g(1)=-\dfrac{1}{5}(1+5)^2\\\\=-\dfrac{1}{5}(6)^2=-\dfrac{1}{5}(36)\\\\=-7.2[/tex]

Hence, g(1) is -7.2.

Answer:

x = 0

Step-by-step explanation:

3(7x − 12) + 26 = 3x − 10

Distribute

21x - 36 +26 = 3x-10

21x -10 = 3x-10

Add 10 to each side

21x = 3x

Subtract 3x from each side

21x-3x = 0

18x =0

x =0

Answer:

0.505 in fraction is 101/200.

it can't be divided into simplest form

Answer:

0

Step-by-step explanation:

Slope is -7--7/1--4

=0/5

=0

Slope of the line passing through (-4,-7) and (1, -7) is equals to 0.

"Slope of a line is defined as the ratio of change in y-coordinates to the change in x-coordinates."

Formula used

Slope = ( y₂ - y₁) / (x₂ - x₁)

According to the question,

Line passing through two points (-4, -7) and ( 1, -7)

x₁ and x₂ are x- coordinates on the line.

y₁ and y₂ are the y-coordinates on the line.

Here,

( x₁ , y₁ ) = ( -4, -7)

(x₂ , y₂) = ( 1 , -7)

Substitute the given value in the formula we get,

Slope = [ -7 -(-7)] / [ 1 - (-4)]

         = (-7 +7) / ( 1 +4)

         = 0 / 5

         = 0  

Hence, slope of the line passing through (-4,-7) and (1, -7) is equals to 0.

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Answer:

see explanation

Step-by-step explanation:

Given A = 3x² + 2y + 2 and B = 6x² - 8y + 1 , then

A + B

= 3x² + 2y + 2 + 6x² - 8y + 1 ← collect like terms

= 9x² - 6y + 3

-------------------------------

A - B

= 3x² + 2y + 2 - (6x² - 8y + 1) ← distribute parenthesis by - 1

= 3x² + 2y + 2 - 6x² + 8y - 1 ← collect like terms

= - 3x² + 10y + 1

Answer:

The two possible distances from Ship A to the distress call boat are 64.4 km and 147.5 km

Step-by-step explanation:

The given parameters are;

The distance between Ship A and Ship B = 120 km

The distance of the distress call from Ship B = 70 km

The angle made between the line from Ship A to B and the line from Ship A to the distress call = 28° = Opposite angle to the line from the location of the distress caller to Ship B

Therefore;

70/(sin(28°)) = 120/(sin(x))

Where;

x = The angle opposite the line from Ship A to B

sin(x) = ((sin(28°))×120)/70 = 0.805

x = sin⁻¹(0.805) = 53.59°

Therefore, the angle opposite the line from Ship A to the distress caller, r = 180 - (28 + 53.59) = 98.4°

From sin rule, we have;

70/(sin(28°)) = r/(sin(98.4°))

r = (70/(sin(28°)))×(sin(98.4°)) = 147.5

However by cosine rule, we have;

70² = 120² + r² - 2×120×r × cos(28°)

4,900 = 14,400 + r² - 211.907·r

r² - 211.907·r + 14,400 - 4,900 = 0

r² - 211.907·r + 9,500 = 0

Factorizing, we have;

[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]

[tex]r = \dfrac{211.907\pm \sqrt{211.907^{2}-4\times 1\times 9,500}}{2\times 1}[/tex]

r = 64.406 km or 147.501 km

Which gives;

The distance of the line from Ship A to the distress caller =  64.4 km or 147.5 km to the nearest tenth.

The two possible distances from Ship A to the distress call boat = 64.4 km and 147.5 km

Answer:

See below!

Step-by-step explanation:

1. 5g + h = g

4g = -h

g = [tex]-\frac{h}{4}[/tex]

2. y = mx + b

y - b = mx

m = [tex]\frac{y - b}{x}[/tex]

3. 3y + z = am - 4y

7y = am - z

y = [tex]\frac{am - z}{7}[/tex]

4. km + 5x = 6y

km = 6y - 5x

m = [tex]\frac{6y - 5x}{k}[/tex]

5. [tex]\frac{3ax - n}{5} = -4[/tex]

3ax - n = -20

3ax = n - 20

x = [tex]\frac{n-20}{3a}[/tex]

6. [tex]\frac{by+2}{3}= c[/tex]

by + 2 = 3c

by = 3c - 2

y = [tex]\frac{3c-2}{b}[/tex]

7. at + b = ar - c

at - ar = -b - c

a(t - r) = -(b + c)

a = [tex]-\frac{b+c}{t-r}[/tex]

Answer:

Solution : y = ± 1/3x

Step-by-step explanation:

Remember that the equation of a hyperbola is in the form (y - k)² / a² - (x - h)² / b² = 1. Therefore we have a² here = 9, and b² here = 81.

To determine the asymptotes we can use the equation y = k ± a/b(x - h). What makes this equation really simple, is that k = 0 and h = 0, giving us y = ± a/b(x). Let's isolate a and b given a² = 9, and b² = 81 --- (1)

a² = 9

a = 3

b² = 81

b = 9

Therefore our asymptotes will be in the form y = ± a/b(x) = ± 3/9(x) = ± 1/3x. Our solution is thus option a.

Answer:

8/5

Step-by-step explanation:

Answer:

V = Vab from the drawing.

So if V = –10 volts, then Vab = –10v and Vba = +10v

"the figure is the same in the link below except that the voltage is from a to b" but the drawing shows that V = Vab

Hoped I helped

Answer:

An equilateral triangle is a triangle in which all three sides are equal. An equilateral triangle is also equiangular, in which all three internal angles are also congruent to each other and are each 60°.

Parallelogram and rhombus possibly.

Trapezoid.

Answer:

Part a)

Three equal sides

Three equal angles

Part b)

1) Rhombus

2) Parallelogram

[Both have 2 pairs of parallel sides and thus have their opposite angles equal]

Part c)

Trapezoid [Have exactly 1 pair of parallel sides]

I hope this helps you

5u+5-5u=u+8

5-8=u

u=-3

Answer:

two

Step-by-step explanation:

A ratio compares the relative sizes of two quantities .​

Answer:2

Step-by-step explanation:

Answer:

The difference in unit price is $0.01/ounce

Step-by-step explanation:

A 16 -ounce bottle of Spring Water = $1.76

A 20 -ounce bottle of Fresh Water = $2.40

For the spring water, the unit price = 1.76/16 = $0.11/ounce

For the fresh water, the unit price = 2.4/20 $0.12/ounce

The difference in unit price is $0.01/ounce

Answer:

[tex] \frac{9}{7} \: or \: 1.28[/tex]

Step-by-step explanation:

[tex] \frac{9}{m + 4} = \frac{9}{3 + 4} = \frac{9}{7} \: or \: 1.28[/tex]

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

So we have the equation:

[tex]6x+2=9x-1[/tex]

Subtract 6x from both sides:

[tex](6x+2)-6x=(9x-1)-6x\\2=3x-1[/tex]

Add 1 to both sides:

[tex](2)+1=(3x-1)+1\\3=3x[/tex]

Divide both sides by 3:

[tex](3)/3=(3x)/3\\x=1[/tex]

So, the value of x is 1 :)

P.S. Welcome to Brainly!

Answer:

  see below

Step-by-step explanation:

For a vertical scale factor of 'b', and a translation by (h, k) in the (right, up) direction, the transformed function is ...

  g(x) = b·f(x -h) +k

For a scale factor of 1/2 and translation left 3 and down 2, the transformed function is ...

  g(x) = (1/2)f(x +3) -2

  g(x) = (1/2)5^(x +3) =2 . . . . matches the 2nd choice

Answer:

30.1 Metres

Step-by-step explanation:

For this problem, we will use the law of sines twice to find the height of the tree.

First, you need to draw the image of the tree with two triangles, one with an angle of 34 degrees, and the second with an angle of 41 degrees, both being a right triangle toward the tree.  The distance between point A and point B should be 10 meters.

From here, your bottom line of the triangle should be represented as 10 + x for the unknown distance from where Sophie stood to the tree.  The x represents the distance from point B to the tree, whereas 10 + x represents the distance from point A to the tree.

Now, let's use the scalene triangle created by the distance between point A and point B to the top of the tree, to calculate the diagonal distance from point B to the top of the tree.

Using this scalene, we have the angles, 34, 7, and 139.  Now, use the law of sines to find the diagonal of point B to the top of the tree represented by r.

sin(7) / 10 == sin (34) / r

r == 10 * sin (34) / sin(7)

r == 10 * .55919 / .12187

r == 45.88

Now that we know this diagonal distance, we can use the law of sines again with the second triangle, 41, 49, 90, to find the height of the tree represented by y.

sin(41) / y == sin(90) / 45.88

y == 45.88 * sin(41) / sin(90)

y == 45.88 * .65606 / 1

y == 30.1

So the height of the tree to the nearest tenth of a metre would be 30.1 metres.

Cheers.

Answer:

Step-by-step explanation:

tan(34°)≈0.6745         tg(41°)≈0.8693

[tex]\tan(34^o)=\dfrac h{x+10}\\\\\tan(34^o)(x+10)=h\\\\x+10=\dfrac h{\tan(34^o)}\\\\x=\dfrac h{\tan(34^o)}-10[/tex]                               [tex]\tan(41^o)=\dfrac hx\\\\x\tan(41^o)=h\\\\x=\dfrac h{\tan(41^o)}[/tex]

[tex]\dfrac h{\tan(34^o)}-10=\dfrac h{\tan(41^o)}\\\\ h\tan(41^o)-10\tan(34^o)\tan(41^o)=h\tan(34^o) \\\\ h\tan(41^o)-h\tan(34^o)=10\tan(34^o)\tan(41^o) \\\\ h[\tan(41^o)-\tan(34^o)]=10\tan(34^o)\tan(41^o)\\\\h=\dfrac{10\tan(34^o)\tan(41^o)}{\tan(41^o)-\tan(34^o)}\\\\\\h\approx \dfrac{10\cdot0.6745\cdot0.8693}{0.8693-0.6745}=\dfrac{5.8634285}{0.1948}\approx30.1\ m[/tex]

Answer:

The odds to get a blackjack (natural) as arrangement: 128 / 2652 = . 0483 = 4.83%. 4.83% is equivalent to about 1 in 21 blackjack hands.

Answer: a = -6

Step-by-step explanation:

Answer:

F=C+32.

128=C+32.

C=128-32.

96°C

Answer:

There was a Horizontal translation left b units and then Vertical stretch or compression

Step-by-step explanation:

Given : [tex]g(x) = a f(x + b)[/tex]

We are supposed to show the transformation

Rule : f(x)→f(x+c)

Horizontal translation left c units

So, f(x+b) is the Horizontal translation left b units

Rule : f(x)→cf(x)

Vertical stretch or compression

So,[tex]g(x) = a f(x + b)[/tex]

So, Initially there was a Horizontal translation left b units and then Vertical stretch or compression

Answer:

-2f(x+4), A

Step-by-step explanation:

Vertically stretch the function by 2, flip it over the x-axis and add 4 to shift right

(The explaination might be BS but the answer is 100% correct, took the quiz)

Answer:

The answer to the equation is 1.

Step-by-step explanation:

When having an algebraic equation, you have to move all of the variables on one side. Therefore, you can move the -2x or the 7x. However, to make a positive number, I would recommend to move the -2x.

To move the -2x to the other side, you add 2x to the both sides of the equation. Since the original equation is 9-2x=7x, you will add the 2x to it, so your equation will now look like this: 9-2x+2x=7x+2x. Once simplifying that down, you will have 9=9x. Then, you can divide the coefficient, so the 9 on the left side, and the 9 on the right side. After this, you will have 1=x. AKA x=1, which is the answer to the equation!

The solution to the equation 9 - 2x = 7x is x = 1 as per the algebraic operations.

To solve the equation 9 - 2x = 7x for x, we need to isolate the variable on one side of the equation. Here's the step-by-step process:

Start by combining like terms. Add 2x to both sides of the equation to move the variable terms to one side:

9 - 2x + 2x = 7x + 2x

9 = 9x

Divide both sides of the equation by 9 to isolate x:

9/9 = 9x/9

1 = x

Therefore, the solution to the equation 9 - 2x = 7x is x = 1.

By performing the necessary algebraic operations, we found that x is equal to 1. This value satisfies the original equation, making it the solution. It's important to check the solution by substituting x = 1 back into the original equation to ensure that it holds true. In this case, when we substitute x = 1 into the equation, we have 9 - 2(1) = 7(1), which simplifies to 7 = 7, confirming that x = 1 is indeed the correct solution.

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Answer: The average number of cases per bid is 599.

Step-by-step explanation:

Given: One week she put together bids for 680 cases, 507 cases, 830 cases, 391 cases, and 587 cases.

Total cases = 680 +  507 + 830 + 391+587

= 2995

Number of bids = 5

Now, average number of cases per bid = [tex]\dfrac{\text{Total cases }}{\text{Number of bids}}[/tex]

[tex]=\dfrac{2995}{5}\\\\=599[/tex]

Hence, the average number of cases per bid is 599.

Answer:

1860

Step-by-step explanation:

First, we need to get to 0.

1240 above sea level.  The distance to 0 is 1240.

Next, below sea level.  The distance to 0 is 620.

So, add 1240 + 620 to find the distance between the 2 numbers.

1860

Hope this helps!!!

Answer:

25 people are not from Germany or France.

Step-by-step explanation:

1. You first want find out what is the number of people from Germany.

So you would find...

2/5 of 75

or

2/5*75= 30 people from Germany

2. Next you want to to find out the number of people from France.

So you would do the following...

75-30=45 (Subtract the number of people from Germany from 75 so you can get the total number of people from France and other countries)

4/9 of 45 to find the number of people from France.

4/9 *45= 20

3. Lastly you need to find the people who are from neither of the countries listed above.

Add 30+20= 50

Then subtract that number from 75.

75-50= 25 people who are from neither France or Germany.

Voila! This is your answer. Hope this helps! :)

Answer:

The complete sequence is: 1, 8, 29, 92, 281.

Step-by-step explanation:

The series to be completed is:

1, _, _, _, _

The information provided is:

Then the nth term can be determined using the expression:

[tex]a_{n}=3a_{n-1}+5[/tex]

Compute the 2nd, 3rd, 4th and 5th term as follows:

[tex]a_{2}=3a_{2-1}+5 = 3a_{1}+5=(3\times 1)+5=8\\\\a_{3}=3a_{3-1}+5 = 3a_{2}+5=(3\times 8)+5=29\\\\a_{4}=3a_{4-1}+5 = 3a_{3}+5=(3\times 29)+5=92\\\\a_{5}=3a_{5-1}+5 = 3a_{4}+5=(3\times 92)+5=281[/tex]

Thus, the complete sequence is:

1, 8, 29, 92, 281.