Write each function in vertex form, and identify its vertex.

14. h(x)=3x^2−24x+53

15. h(x)=x^2 +8x−10

16. g(x)=x^2 −3x+16

17. h(x)=3x^2 −12x−4

Answer:

The coordinates of [tex]P^\prime[/tex] would be [tex](3,\, 0)[/tex].

Step-by-step explanation:

The two points [tex]P[/tex] and [tex]P^\prime[/tex] are on a Cartesian plane.

By convention, the positive [tex]x[/tex]-axis on a Cartesian plane points to the right. As a result,

Also by convention, the positive [tex]y[/tex]-axis on a Cartesian plane points upwards. Similarly,

In this case,

Therefore, the coordinates of [tex]P^\prime[/tex] would be [tex](3,\, 0)[/tex].

Answer:

(3,0)

Step-by-step explanation:

The two points  and  are on a Cartesian plane. By convention, the positive -axis on a Cartesian plane points to the right. As a result,Moving a point to the right by  units is the same as adding  to its -coordinate. If the point was initially at , it would be moved to .Moving a point to the left by  units is the same as subtracting  from its -coordinate. If the point was initially at , it would be moved to .Also by convention, the positive -axis on a Cartesian plane points upwards. Similarly, Moving a point upwards by  units is the same as adding  to its -coordinate. If the point was initially at , it would be moved to .Moving a point downwards by  units is the same as subtracting  from its -coordinate. If the point was initially at , it would be moved to .In this case, Point  was initially at . is at  after it is moved to the left by  units. That's the same as . is at  after it is moved upward by  units. That's the same as .Therefore, the coordinates of  would be .

Answer: 1096cm^2

Step-by-step explanation: 2(17x14+ 17x10+ 10x14)

Answer:

18

Step-by-step explanation:

one half times (four plus eight)

Writing mathematically

1½ ( 4+8)

Using BODMAS

we'll take the bracket first

1½ × 12

Change 1½ to improper fraction = 3/2

3/2 × 12 = 3×6

= 18

I hope this was helpful, please mark as brainliest

Answer: 6.

Step-by-step explanation: First, answer the question in the brackets, that equals 12. Take the 12 and multiply it by 1/2. When you do this, you are basically dividing it by 2, which gives you 6.

Hope this helps!

Answer:

[tex]x \: < \: 3\: and \: x\: > \: 2[/tex]

Step-by-step explanation:

The given inequality is

[tex]4x - 4 \: < \: 8 \: and \: 9x + 5 \: > \: 23[/tex]

Add 4 to both sides of the first inequality and subtract 5 from both sides of the second inequality.

[tex]4x \: < \: 8 + 4 \: and \: 9x\: > \: 23 - 5[/tex]

We simplify to get:

[tex]4x \: < \: 12 \: and \: 9x\: > \: 18[/tex]

Divide through the first inequality by 4 and the second by 9.

[tex]x \: < \: 3\: and \: x\: > \: 2[/tex]

Answer:

The graph of

[tex]y = \frac{2.5}{x} [/tex]

us a vertical stretch of the graph of

[tex]y = \frac{1}{x} [/tex]

by a factor of 2.5.

Step-by-step explanation:

The given functions are

[tex]y = \frac{1}{x} [/tex]

and

[tex]y = \frac{2.5}{x} [/tex]

The graph of

[tex]y = \frac{1}{x} [/tex]

is the parent rational function.

The graph of

[tex]y = \frac{2.5}{x} [/tex]

is a vertical stretch of the parent rational function by a factor of 2.5

Answer:

13.89 Dollars

Step-by-step explanation:

Add 47.72 and 3.39

51.11

Subtract that answer from 65

13.89

Answer:

($13.39 mistype) $13.89

Step-by-step explanation:

65 - 47.72 = 17.28

17.28 - 3.39 = 13.89

The answer is $13.89. Don't feel ashamed you don't know the answer. Have you considered tutoring?

Answer:

The total cost is $34.24.

Step-by-step explanation:

Given : Bob is looking to buy a new baseball cap with his favorite team’s logo on it. He finds one that normally sells for $32. If a 7% sales tax is added.

To find : What is the total cost?

Solution :

The sales price = $32

The tax rate = 7%=0.07

The sales tax is given by,

[tex]\text{Sales tax}=\text{Rate}\times \text{Price}[/tex]

[tex]\text{Sales tax}=0.07\times 32[/tex]

[tex]\text{Sales tax}=2.24[/tex]

Now, adding to sales price

Total cost = 32+2.24

Total cost = $34.24

Therefore, the total cost is $34.24.

Answer:

  Dee won

Step-by-step explanation:

Using < to mean "finished ahead of ", we are given ...

  B = 3

  D < B

  D < C

  A < C

  D < A

Dee finished ahead of Air, Bart, and Caper, so Dee won the race.

_____

The order of finish must be D, A, B, C.

Slope is 4.5 or 9/2

Step-by-step explanation:

y = 4.5 x

∴ Slope, m = 4.5 or 9/2

Answer:

If the ratio is cavities to volume, you need cavities/V where V is some sort of volume.  cm^3 is a volume.

Step-by-step explanation:

Answer:

I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

Step-by-step explanation:

The number of total objects collected by me  = 20

The number of objects collected by my friend  = 20

Let us assume:

The number of rocks collected by me  = m

The number of fossils collected by me  = 2 k

⇒ m +  2 k =  20  .... (1)

So, according to the question:

The number of rocks collected by my friend = 3 x (rocks collected by me)  

= 3 x (m)  = 3 m

The number of fossils collected by my friend = 1/2 x (fossils collected by me)    = 1/2 x (2k )  = k

⇒ 3 m +   k =  20  .... (2)

Solving (1)and (2) for the value of m and k, we get:

m +  2 k =  20     ⇒ m = 20 - 2 k ... Put this in (2)

3 m +   k =  20  ⇒  3 (20 - 2 k) +  k = 20

⇒ 60 - 6 k +  k  = 20

or, - 5k = -40

or, k = 40/5  = 8

⇒ k= 8

m + 2(8)  = 20

or, m = 4

Hence, the number of rocks collected by me  = m = 4

The number of fossils collected by me  =  2 k = 2 (4)  = 16

Hence, the number of rocks collected by my friend   = 3 m  = 3 x 4 = 12

The number of fossils collected by my friend   =   k =  8

Hence, I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.

You collect 4 rocks and 16 fossils. Your friend collects 12 rocks and 8 fossils.

You and your friend each collect 20 objects. Let's define our variables:

Let R represent the number of rocks you collect. Let F represent the number of fossils you collect.

You collect 20 objects in total:

R + F = 20

Your friend collects three times as many rocks and half as many fossils as you:

Rocks: 3R Fossils: F / 2

Your friend also collects 20 objects in total:

3R + F / 2 = 20

We have two equations:

R + F = 20 and 3R + F / 2 = 20

First, solve equation 1 for F:

F = 20 - R

Next, substitute this into equation 2:

3R + (20 - R) / 2 = 20

Multiply everything by 2 to clear the fraction:

6R + 20 - R = 40

Simplify:

R + 20 = 40

Subtract 20 from both sides:

5R = 20

Divide by 5:

R = 4

Now, substitute R back into the equation for F:

F = 20 - 4

F = 16

Then, 3R= 12 and F/2 = 8

Thus, you collect 4 rocks and 16 fossils.  Your friend collects 12 rocks and 8 fossils.

full timers work 5 hours a day whereas Part timers work 3 hours a day!

Step-by-step explanation:

Here we have , The difference in hours between full times and the part timers to work three hours a day is 2 working hours  . We need to find that  how many hours per day to full timers work . Let's find out:

Let full timers work x hours , Part time workers work 3 hours a day , According to question, difference in hours between full times and the part timers to work three hours a day is 2 working hours  i.e.

⇒ [tex]x-3 = 2[/tex]

Adding 3 to make x term alone :

⇒ [tex]x-3+3 = 2+3[/tex]

⇒ [tex]x=5[/tex]

Therefore, full timers work 5 hours a day whereas Part timers work 3 hours a day!

Step-by-step explanation:

[tex] \sqrt[8]{ {x}^{2} {y}^{6} } \\ \\ = ( {x}^{2} {y}^{6} )^{ \frac{1}{8} } \\ \\ = {x}^{2 \times \frac{1}{8}} {y}^{6\times \frac{1}{8}} \\ \\ = x^{\frac{1}{4}} {y}^{3\times \frac{1}{4}} \\ \\ = x^{\frac{1}{4}} {y}^{\frac{3}{4}} \\ \\ = \sqrt[4]{x {y}^{3} } \\ [/tex]

Final answer:

[tex]\(\sqrt[8]{x^2 y^6} = x^{\frac{1}{4}} y^{\frac{3}{4}}\)[/tex] This is the expression in its simplest radical form.

Explanation:

To simplify the given expression [tex]\sqrt[8]{x^2 y^6}[/tex], we must consider the rules for radicals and exponents.

Recall that [tex]\(\sqrt[n]{a^m} = a^{\frac{m}{n}}\)[/tex], assuming [tex]\(a\geq0\)[/tex] when n is even. Breaking down the radicals, we can rewrite the expression as:

Since both terms are under the same radical, we can multiply them together:

[tex]\(\sqrt[8]{x^2 y^6} = x^{\frac{1}{4}} y^{\frac{3}{4}}\)[/tex]

This is the expression in its simplest radical form.

The area of the shaded region is 0.7257.

The area of the shaded region represents the probability that a standard normal variable will be less than 0.74.

Since the standard normal distribution is symmetrical, the area less than -0.74 is equal to the area greater than 0.74, which can be found using the standard normal table or a calculator.

Using the standard normal table, we find that the area less than -0.74 is 0.2743.

Therefore, the area greater than 0.74 is also 0.2743.

The total area under the curve is 1, so the area less than 0.74 is 1 - 0.2743 = 0.7257.

Complete Question:

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation.

Step-by-step explanation:

[tex]x + 15 \degree = 102 \degree \: \\ (corresponding \: \angle s) \\ \therefore \: x = 102 \degree - 15 \degree \\ \huge \red { \boxed{\therefore \: x = 87 \degree}}[/tex]

The value of x according to the relationship between the angles is; x= 87°

By mathematical convention, Corresponding angles (otherwise called F-angles) are equal.

On this note; the angle 102° and x +15° are equal.

Therefore,

x = 87°.

Read more on corresponding angles;

https://brainly.com/question/2009183

Final answer:

The model diameter of the bicycle wheel is found using the scale factor of 1:5 and the actual diameter of 24 inches (2 feet). By setting up a proportion and solving for the model diameter, we find it to be 4.8 inches.

Explanation:

To find the missing diameter of the bicycle wheel model when given the actual diameter and a scale factor, we use a proportion:

The scale is given as 1:5, which means 1 unit on the model represents 5 units in reality. First, we need to convert the actual diameter of 2 feet into inches because the model's diameter will be given in inches. There are 12 inches in 1 foot, so 2 feet is 24 inches.

After calculating, the model diameter is 4.8 inches.

Area of the figure is 71.13

Step-by-step explanation:

Find the area of the semicircle. Here, radius = 3.

Area = 1/2 πr² = 1/2 × 3.14 × 3² = 14.13

Area = length × width = 8 × 6 = 48

Area = 1/2 × base × height = 1/2 × 3 × 6 = 9

Area of the figure = 14.13 + 48 + 9 = 71.13

Answer:

The probability that I mist sample 5 12-year-olds to find the first one who can pick out Colorado on a map is 1.  

Step-by-step explanation:

The research suggests that about 24% of 12-year-olds in the US can pick out the state of Colorado on a map. The probability always exceeds the probabilities of picking out 1 over 5 12-year-olds, which is 20%, in a sample is well-represented the 12-year-old population of the US. Hence, the answer is 1 (or 100%).

Answer:

interest is $255

Step-by-step explanation:

Answer:$255

Step-by-step explanation:

Principal(p)=$1000

Rate(r)=8.5%

Time(t)=3years

Simple interest(SI)=?

SI=(pxrxt)/100

SI=(1000x8.5x3)/100

SI=25500/100

SI=$255

Answer:

63ft

Step-by-step explanation:

area=basexheight so 7x9 which is 63

Answer:

If the hands are at 12 and 3 you would have 1/3

Step-by-step explanation:

At 12 and 3 the hand will take up a third of the clock because at 12 and 3 the clock hands will have a portion of the clock taken up

The fraction of the clock represented when the hands are at 12 and 3 is 1/4.

A fraction is a mathematical term that represents a part of a whole. It is written in the form of a numerator over a denominator, separated by a horizontal line. The numerator represents the part of the whole that is being considered, while the denominator represents the total number of equal parts that make up the whole.

If the hands of a clock are at 12 and 3, then the hour hand is pointing directly at the 3, while the minute hand is pointing directly at the 12.

The fraction of the clock represented by this configuration is the fraction of the total circumference of the clock that is between the 12 and the 3.

Since there are 12 hour markings on a clock face, each hour marking represents 1/12 of the total circumference. Therefore, the distance between the 12 and the 3 is 3/12 or 1/4 of the total circumference.

So, the fraction of the clock represented when the hands are at 12 and 3 is 1/4.

Learn more about Fraction here:

https://brainly.com/question/10354322

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Answer:

[tex]\large\boxed{x^2-4}[/tex]

Step-by-step explanation:

Here we have a Difference of Two Squares:

[tex](a-b)(a+b)=a^2-b^2[/tex]

[tex]\therefore (x - 2)(x+2)=x^2-4[/tex]

Once the standard form of a polynomial is when terms are ordered from the biggest exponent to the lowest exponent,

The polynomial in standard form is [tex]x^2-4[/tex]

Answer:

2x(x - 1)(x + 1)

Step-by-step explanation:

2x³ - 2x

2x(x² - 1)

2x(x - 1)(x + 1)

Answer:

the answer is 2x(x+1)(x-1)

Step-by-step explanation:

Answer:

35.

So that we have:

KLN = 54          JKN =36

LKN = 72          NMJ = 18

KNM = 126       JLM = 72

LJM = 90          KLM = 126

36.

CE = 6√13

37.

m∠Z = 88°

38.

m∠GFE = 85

Step-by-step explanation:

35.

As KLMN is a kite:

+) KL = KN

=> Triangle KLN is  an isosceles triangle.

=> m∠KLN = m∠ KNL = m∠KNJ = 54°

In triangle KLN, total measure of three internal angles are 180 degree, so that: m∠KLN + m∠ KNL + m∠ LKN = 180°

=> 54 + 54 + m∠ LKN = 180°

=> m∠ LKN = 180 - 54 - 54 = 72°

+) KM is the bisector of both Angle LKN and Angle LMN

So that we have:

+) KM and LN is perpendicular to each other at point J

=> m∠LJM = 90°

+) m∠KLM = m∠KNM; m∠KLM + m∠KNM + m∠LKN + m∠LMN = 360°

=> m∠KLM + m∠KLM + 72 + 36 = 360

=> 2 m∠KLM = 360 - 72 - 36 = 252

=> m∠KLM = 252/2 = 126 = m∠KNM

+) We have: m∠KLM = m∠KLN + m∠JLM

=> m∠JLM = m∠KLM - m∠KLN = 126 - 54 = 72

36.

As BCDE is a kite, we have:

+) BC = BE; CD = DE = 21

+) BD is perpendicular to CE and intersect each other point F

=> Angle CFD = 90

=> Triangle CFD is the right triangle

According to Pythagoras theorem: CF^2 + DF^2 = CD^2

=> CF^2 = CD^2 - DF^2  = 21^2 - 18^2 = 441 - 324 = 117

=> CF = [tex]\sqrt{117} =3\sqrt{13}[/tex]

+) According to the feature of a kite shape, F is midpoint of CE

=> CF = FE = 1/2 x CE

=>CE = 2 x CF = 2 x [tex]3\sqrt{3} = 6 \sqrt{13}[/tex]

So that CE = 6√13

37.

As given, WXYZ is a kite shape.

According to the feature of a kite shape, angle ZWX and angle ZYX are equal to each other.

=> ∠ZWX = ∠ZYX

=> 8x -23 = 6x +11

=> 8x - 6x = 11 + 23

=> 2x = 34

=> x = 34/2 = 17

=> ∠ZWX = 8x - 23 = 8*17 - 23 = 113°

=> ∠ZWX = ∠ZYX = 113°

As WXYZ is a kite shape, so that total measure of 4 internal angles of it are 360 degree

So that we have:

∠Z + ∠ZWX + ∠ZYX + ∠WXY = 360

=> ∠Z + 113 + 113 + 46 = 360

=> ∠Z = 360 -113 -113-46 = 88°

So that the measure of ∠Z is 88°

38.

As GDEF is a kite shape. As we can see, GE is the longer diagonal, so that it is the bisector of both Angle DGF and Angle DEF.

H is on GE and GE is the bisector of Angle DEF, so we have:

m∠HEF = m∠GEF = 1/2. m∠DEF = 1/2 . (12x- 16)= 6x - 8

As GDEF is a kite shape so that the two diagonals DF and GE are perpendicular to each other, so that: m∠EHF = 90

In the triangle EHF, m∠EHF = 90

=> EHF is a right triangle

=> m∠HEF + m∠EFH = 90

=> 6x - 8 + 3x -1 = 90

=> 9x = 90 + 8 + 1 = 99

=> x = 99/9 =11

=> m∠HEF = 6x - 8 = 6*11 - 8 = 58 = m∠GEF

GE is the bisector of both Angle DGF

=> m∠EGF = 1/2. m∠DGF = 1/2 . 74 = 37

In the triangle GEF, total measure of three internal angles are 180

=> m∠GFE + m∠EGF + m∠GEF = 180

=> m∠GFE + 37 + 58 = 180

=> m∠GFE = 85

Step-by-step explanation:

Given is a 45°-45°-90 ° angled triangle.

By 45°-45°-90 ° angled triangle theorem:

side opposite to 45° angle is [tex] \frac{1}{\sqrt 2} [/tex] times of hypotenuse.

[tex] \therefore \: 7 = \frac{1}{ \sqrt{2} } \times m \\ \\ \huge \red{ \boxed{\therefore \: m \: = 7 \sqrt{2} \: units}} \\ \\ n \: = \frac{1}{ \sqrt{2} } \times m \\ \\ \therefore \:n \: = \frac{1}{ \sqrt{2} } \times 7 \sqrt{2} \\ \huge \purple{ \boxed{\therefore \:n \: = 7 \: units}} \\ [/tex]

Answer:

Bayes' theorem, was named after a  British mathematician from the 18th-century named Thomas Bayes. The Bayes´ theorem is a mathematical formula for determining conditional probability. The theorem provides a way to revise any existing predictions or theories, and given new or additional evidence. It updates probabilities.

Hope it helps answer the question:)

Final answer:

Bayes' Theorem is a principle in statistics used to update the probability of a hypothesis in light of new evidence. It combines prior knowledge with observed data to estimate probabilities, and is widely applicable in different fields for making informed decisions.

Explanation:

Understanding Bayes' Theorem

Bayes' Theorem is a fundamental concept in the field of probability and statistics. It offers a way to revise existing predictions or theories in light of new evidence. Bayes' theorem states that the probability of A occurring given that B has occurred is P(A|B) = P(A and B) / P(B). In Bayesian analysis, this is often expressed as the probability of a hypothesis given observed data. The formula can be expanded to include prior knowledge by considering the probability of the hypothesis before observing the data, P(A), and the likelihood of observing the data given the hypothesis, P(B|A).

The theorem has extensive applications across various fields, including science, engineering, and even history. For instance, it can be utilized for the estimation of probabilities of unobserved traits, such as determining the age of individuals based on skeletal indicators. By considering prior knowledge and observed data, Bayes' theorem provides a powerful tool for updating beliefs and making informed decisions.

In practice, Bayesian approaches can incorporate prior information that quantifies existing knowledge about a parameter, which can lead to greater certainty in parameter estimates. The use of Bayesian models is often facilitated by software like WinBUGS, which helps in applying complex Bayesian methods to practical problems

Answer:

153 units^2

Step-by-step explanation:

Formula for area of a trapezoid is: A=(b1+b2)*1/2*h

b1=10

b2=24

h=9

Thus:

A=(10+24)*1/2*9

A=34*1/2*9

A=17*9

A=153

So the area of the trapezoid is 153 units^2

Answer: 153

step by step Explanation

Answer:

X=5m-6

Step-by-step explanation:

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

Step 1:  Simplify

[tex]\frac{45}{100}[/tex]

[tex]\frac{45 / 5}{100/5}[/tex]

[tex]\frac{9}{20}[/tex]

Answer:  [tex]\frac{9}{20}[/tex]

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

means 45/100

the common factors that go into both 45 and 100 is 5

hence divide 45 and 100 by 5

[tex]\frac{45/5}{100/5}[/tex]

= [tex]\frac{9}{20}[/tex]