Factor d^2-10d+10 by grouping

The algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)

Translation is the way of changing the position of an object on an xy plane.

If the coordinate points (x, y) is translated  8 units to the left and 12 units up, the resulting coordinate will be:

(x, y) -> (x - 8, y +12)

Hence the algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)

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Answer:

P = 110N + 1,900.

$4,540.

Step-by-step explanation:

Her base salary is $1,900, so your constant/y-intercept for the equation is $1,900.

She makes an additional $110 for each copy, so your slope is $110.

P (the total pay) = 110 * the number of copies sold + 1,900

P = 110N + 1,900.

She sells 24 copies.

P =  110 * 24 + 1,900

P = 2,640 + 1,900

P = 4,540.

So, her total pay is $4,540.

Hope this helps!

Answer:

40091.

Step-by-step explanation:

Multiply 40.091 by 10 three times to get the answer.

40.091 * 10 = 400.91

400.91 * 10 = 4009.1

4009.1 * 10 = 40091.

The expression 40.091 x 10³ can be represented as 40091.

The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.

In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.

Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.

Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.

∴ The expression 40.091 x 10³ can be represented as 40091.

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Answer:

3 grams will be left after 6 half-lives

Step-by-step explanation:

Half-live:

Time it takes for the substance to be reduced by hall.

After n half lives:

The amount remaing is:

[tex]A(n) = A(0)(0.5)^{n}[/tex]

In which A(0) is the initial amount and n is the number of half-lives.

Starting with 210 grams of a radioactive isotope, how much will be left after 6 half-lives?

This is A(6) when A(0) = 210. So

[tex]A(n) = A(0)(0.5)^{n}[/tex]

[tex]A(6) = 210(0.5)^{6} = 3.3[/tex]

Rounding to the nearest gram

3 grams will be left after 6 half-lives

Answer:

60 cm

Step-by-step explanation:

You need to use ratios to solve.  If the scale is 1:30 then the wheel is 2:(?).  Cross-multiply the fractions and solve for x.

1/30 = 2/x

1x = 30*2

x = 60

The wheel is 60 cm in diameter.

Answer:

60 centimeters

Step-by-step explanation:

The scale is 1:30. The wheel diameter is 2 while the actual size of the wheel is unknown. Therefore, the scale for the wheel is 2:x

Let’s set up a proportion.

1/30=2/x

First, cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the numerator of the second by the denominator of the first.

1*x= 2*30

1x=20*30

x=20*30

x=60

Add appropriate units, in this case centimeters (cm).

x= 60 cm

The actual diameter of the wheel is 60 centimeters.

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex] \frac{42}{100} \times 350 = 147[/tex]

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

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Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer:

236

Step-by-step explanation:

The interquartile range is the right edge of the box minus the left edge of the box

The right edge of the box is 301

The left edge of the box is 65

301 -65 =236

The interquartile range is 236

Answer:

65

Step-by-step explanation:

To find interquartile range, you substract upper quartile( 130 in this problem) and the lower quartile(65 in this problem)

Finally, you get the answer 65.

Hope this helps!

Answer:

Step-by-step explanation:

Let the measure of third angle be X

The sum of interior angle of triangle = X

Let's create an equation

[tex]x + 32 + 90 = 180[/tex]

Add the numbers

[tex]x + 122 = 180[/tex]

Move constant to R.H.S and change its sign

[tex]x = 180 - 122[/tex]

Subtract the numbers

[tex]x = 58[/tex] °

Hope this helps...

Best regards!!

Answer:

Step-by-step explanation:

To decipher how many eggs you have left, we must read the statement well.

I have 5 eggs if I break 2 eggs it is to cook them and when they are cooked they will be eaten, so we simply do the following:

5 -2= 3

Now you only have 3 eggs left.

Step-by-step explanation:

Given:

5 eggs

Required:

Number of eggs after breaking, cooking and eating 2.

Solution:

I won't count the eggs as 6.

Broken=cooked=eaten=2

5-2=3

Hope it helps ;) ❤❤❤

Answer:

0.99865

Step-by-step explanation:

The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.

To solve the above question, we would be using the z score formula

The formula for calculating a z-score

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

In the above question,

x is 115 liters

μ is 100

σ is the population standard deviation is unknown. But we were given variance in the question.

Standard deviation = √Variance

Variance = 9

Hence, Standard deviation = √9 = 3

We go ahead to calculate our z score

z = (x-μ)/σ

z = (115 - 100) / 3

z = 15/ 3

z score = 5

Using the z score table of normal distribution to find the Probability of having a z score of 5

P(x = 115) = P(z = 5) =

0.99865

Therefore the probability that this year it will produce 115 liters of wine = 0.99865

Answer: C

Step-by-step explanation:

G(F(x)) means F(x) is being plugged into every x in G(x). Since we are given the G(x) and F(x) functions, we can directly plug 2x-5 into x²+1.

G(F(x))=G(2x-5)

G(F(x))=(2x-5)²+1                            [use FOIL method to expand (2x-5)²]

G(F(x))=(4x²-10x-10x+25)+1           [combine like terms]

G(F(x))=4x²-20x+26

Now that we have found G(F(x))=4x²-20x+26, we know that the answer is C.

Answer:

1. can

2. less

3. 5

Step-by-step explanation:

To find out if Waclaw could make it to the gas station using 10 miles, we need to add the number of miles he has to go in order to reach his destination.

[tex]4\frac{7}{8}+4\frac{3}{4} = 9\frac{5}{8}\\[/tex]

9 5/8 is less than 10, so he can make it to the gas station.

We can also find out the answer without even adding the numbers together, because both values are less than five, and when that happens, the sum cannot be 10 or more, so Waclaw can make it to the gas station.

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!

Answer:

79 degrees

Step-by-step explanation:

There's a bunch of theorems you have to memorize.

This is an inscribed angle.

The measure of angle RST is 1/2 of the intercepted arc.

<RST = 1/2(158) = 79

Answer:

We accept H₀

p-value = 0,1618

Step-by-step explanation:

We are going to solve a one tail proportion-test ( right tail)

We assume Normal distribution

Sample population 1000

Political strategist to test  wants to test:

Null hypothesis                             H₀           p = p₀       or   p = 26 %

Alternate hypothesis                    Hₐ           p > p₀        or  p > 26%

We assume CI  90 % then

α = 10 %     α = 0,1    and  z score for α = 0,1  is critical value

z = 2,32          ( note  2,32 is z score for α = 0,1017 "good approximation")

To compute z(s)

z(s)  =  ( p -p₀ ) / √ p₀q₀/n

z(s)  =  ( 0,29 - 0,26 ) /√ 0,26*0,74/1000

z(s)  = 0,03 / 0,014

z(s) = 2,14

We compare z(s) and z(c)

z(s) < z(c)

2,14 < 2,32

z(s) is in the acceptance region we accept H₀

The p-value for z(s) is from z-table

p-value = 0,1618

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Answer:

b. the approx time it takes an investment to double in value

Answer:

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220

The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.

Adult's ticket = [y]

Children's ticket = [x]

Student's ticket = [z]

and

y = 3x

Now -

x + y + z = 500

x + 3x + z = 500

4x + z = 500       ....[1]

and

12x + 18y + 15z = 8040

12x + 18(3x) + 15z = 8040

12x + 54x + 15z = 8040

66x + 15z = 8040     ....[2]

On solving [1] and [2], we get -

x = 90 and z = 140

and

y = 3x = 3 x 90 = 270

y = 270

Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

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Answer:7

Step-by-step explanation:

Answer:

X=7

Step-by-step explanation:

made a 100 on my quiz but i dont feel like puting my work in here and typing it

Answer:

The probability that the person is between 65 and 69 inches is 0.5403

Step-by-step explanation:

Mean height = [tex]\mu = 66[/tex]

Standard deviation = [tex]\sigma = 2.5[/tex]

We are supposed to find What is the probability that the person is between 65 and 69 inches i.e.P(65<x<69)

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

At x = 65

[tex]Z=\frac{65-66}{2.5}[/tex]

Z=-0.4

Refer the z table for p value

P(x<65)=0.3446

At x = 69

[tex]Z=\frac{69-66}{2.5}[/tex]

Z=1.2

P(x<69)=0.8849

So,P(65<x<69)=P(x<69)-P(x<65)=0.8849-0.3446=0.5403

Hence the probability that the person is between 65 and 69 inches is 0.5403

Answer:

The length of BC is √105 cm or 10.2 cm.

Step-by-step explanation:

You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :

[tex] {c}^{2} = { a}^{2} + {b}^{2} [/tex]

[tex]let \:a =BC \:, \: b = 8 \: , \: c = 13[/tex]

[tex] {13}^{2} = {BC}^{2} + {8}^{2} [/tex]

[tex]169 = {BC}^{2} + 64[/tex]

[tex] {BC}^{2} = 169 - 64[/tex]

[tex] {BC}^{2} = 105[/tex]

[tex]BC = \sqrt{105} [/tex]

[tex]BC = 10.2 \: cm \: (3s.f)[/tex]

Answer:

[tex] \boxed{\sf Length \ of \ BC = \sqrt{105} \ cm} [/tex]

Given:

AB = 13 cm

AC = 8 cm

To Find:

Length of BC

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore \\ \sf {AC}^{2} + {BC}^{2} = {AB}^{2} \\ \sf \implies {8}^{2} + {BC}^{2} = {13}^{2} \\ \\ \sf {8}^{2} = 64 : \\ \sf \implies 64 + {BC}^{2} = {13}^{2} \\ \\ \sf {13}^{2} = 169 : \\ \sf \implies 64 + {BC}^{2} = 169 \\ \\ \sf Substract \: 64 \: from \: both \: sides : \\ \sf \implies (64 - 64) + {BC}^{2} = 169 - 64 \\ \\ \sf 64 - 64 = 0 : \\ \sf \implies {BC}^{2} = 169 - 64 \\ \\ \sf 169 - 64 = 105 : \\ \sf \implies {BC}^{2} = 105 \\ \\ \sf \implies BC = \sqrt{ 105 } \ cm [/tex]

So,

Length of BC = [tex] \sqrt{105} [/tex] cm

Answer:

Look for perpendicular lines or corresponding angles or alternate interior angles.

Step-by-step explanation:

When you want to show that a quadrilateral is a parallelogram you need to show that the oposite sides are parallel. In order to show that two segments are parallel there are various theorems and definitions you can use.

1 -  Remember that two lines perpendicular to the same segment are parallel.

2 - When two lines are cut by a secant and their alternate interior angles are congruent, then the resulting lines are parallel, I will attach a drawing to illustrate what I am saying.

3 - When two lines are cut by a secant and their CORRESPONDING angles are congruent, then the resulting lines are parallel, I will also attach a drawing to illustrate what I am saying.

Answer:

Step-by-step explanation:

Using the formula for calculating the distance between two points to calculate the length of WX.

D = √(y₂-y₁)²+(x₂-x₁)²

Given the endpoints W(2,-7) and X(5,-4), x₁ = 2, y₁ = -7, x₂ = 5 and y₂ = -4

Substituting this values into the formula to get the length of WX will give;

WX = √(-4-(-7))²+(5-2)²

WX = √(-4+7)²+3²

WX = √3²+3²

WX = √18

WX = √2*9

WX = 3√2 units

Hence the length of WX is 3√2 units.

Answer:

3[tex]\sqrt{2}[/tex]

Hope this helps!

Step-by-step explanation:

Answer: 12-i

               12-(√-1)

Step-by-step explanation:

[tex]18-\sqrt{-25}[/tex]   Original Question

[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex]   Split

[tex]18-5*(\sqrt{-1} )[/tex]   Solve for square root

[tex]12-\sqrt{-1}[/tex]   Subtract

You can substitute [tex]\sqrt{-1}[/tex] for i

[tex]12-i[/tex]   Substitute

Answer:

18-5i

Step-by-step explanation:

Greetings from Brasil...

The equation is:

putting COS X for the 2nd member

- √(1 - 3.COS² X) = - COS X     ×(- 1)

√(1 - 3.COS² X) = COS X          everything squared

[√(1 - 3.COS² X)]² = (COS X)²

1 - 3.COS² X = COS² X

1 - 3.COS² X - COS² X = 0

1 - 4.COS² X = 0

making Y = COS X

1 - 4Y² = 0

- 4Y² = - 1     ×(- 1)

4Y² = 1

Y² = 1/4

Y = ±√1/4

Y = ± 1/2    

so, as we saw above

Y = COS X

1/2 = COS X   and   - 1/2 = COS X

so to get COS X = ± 1/2, then

X = π/3 = 60         (cos +)

X = 2π/3 = 120      (cos -)

X = 4π/3 = 240    (cos -)

X = 5π/3 = 300     (cos +)

So the only option that includes + and - its:

60° + n360° , 120° + n360°

The above question is not complete because it was not written and arranged properly

Complete Question

1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.

2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.

3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.

Answer:

1) Volume of the cone = 134.04cubic units

2)Volume of the cylinder = 402.12cubic units

3) Volume of the sphere= 268.08 cubic units. Hence, if a sphere has the same radius as the cylinder, its volume is 2/3 times the volume of the cylinder.

Step-by-step explanation:

1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.

Volume of a cone = 1/3πr²h

h = 8 units

r = 4 units

Volume = 1/3 × π × 4² × 8

134.04cubic units

2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.

Volume of a cylinder = πr²h

Height and radius is the same as that of the cones hence,

h = 8 units

r = 4 units

= π × 4² × 8

= 402.12cubic units.

3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.

Volume of a Sphere = 4/3πr³

r = radius of the cylinder = 4 units

Volume of a Sphere = 4/3 × π × 4³

= 268.08 cubic units.

From the above question, we are asked to compare the volume of the sphere with the volume of the cylinder

Volume of the sphere : Volume of the cylinder

268.08 cubic units : 402.12 cubic units

268.08/402.12 = 2/3

Therefore, the volume of the sphere is 2/3 times the volume of the cylinder