Adam solved this equation and identified the number of solutions.

24x – 22 = 4(6x – 1)

24x – 22 = 24x – 4

24x = 24x + 18

0 = 18

The equation has infinitely many solutions
what is his mistake

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}

Step-by-step explanation:

we have

[tex]f(x)=-x^{2}-2x+15[/tex]

This is the equation of a vertical parabola open downward

The vertex is a maximum

Find the vertex of the quadratic equation

[tex]f(x)-15=-x^{2}-2x[/tex]

[tex]f(x)-15=-(x^{2}+2x)[/tex]

[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]  

[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]

[tex]f(x)-16=-(x^{2}+2x+1)[/tex]

[tex]f(x)-16=-(x+1)^{2}[/tex]

[tex]f(x)=-(x+1)^{2}+16[/tex] -----> equation in vertex form

The vertex is the point (-1,16)

therefore

The domain is the interval ----> (-∞,∞)  All real numbers

The range is the interval ----> (-∞,16]  All real numbers less than or equal to 16

Answer:

The Answer Is B

Step-by-step explanation:

domain is all real numbers. The range is {y|y ≤ 16}.

Answer:

x = 9.6

Step-by-step explanation:

The figure is a similar figure and the quadrilaterals (4 sides) created are related to each other by the same ratio.

So we can say:

8 goes with x as (8+12) goes with 24

We can setup a ratio and solve for x:

[tex]\frac{8}{x}=\frac{8+12}{24}\\\frac{8}{x}=\frac{20}{24}\\20x=8*24\\20x=192\\x=\frac{192}{20}\\x=9.6[/tex]

So x = 9.6

The value of x in the figure drawn is 9.6

we can create a proportional expression thus :

8 = x

(8 + 12) = 24

This means

8 = x

20 = 24

cross multiply

20x = 24 × 8

20x = 192

divide both sides by 20 to isolate x

x = 192/20

x = 9.6

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Answer:

[tex]\large\boxed{h=\dfrac{3V}{\pi r^2}}[/tex]

Step-by-step explanation:

[tex]V=\dfrac{1}{3}\pi r^2h\to\text{It's the formula of a volume of a cone}\\\\\text{Solve for}\ h:\\\\\dfrac{1}{3}\pi r^2h=V\qquad\text{multiply both sides by 3}\\\\\pi r^2h=3V\qquad\text{divide both sides by}\ \pi r^2\\\\h=\dfrac{3V}{\pi r^2}[/tex]

Answer:

opposite angles in parralelograms are congruent

Step-by-step explanation:

Answer:

equal

Step-by-step explanation:

Opposite angles in parallelograms are equal.

Answer:

C

Step-by-step explanatio

33 + 33 + 38 + 35 +37 + 40 + 57 = 273

273 / 7 = 39

33 + 33 + 38 + 35 +37 + 40 = 216

216 / 6 = 36

The mean (average) of the data set without the outlier is 36 and including the outlier is 39. The outlier here being the value 57 which deviates most from the other values in data set.

To find the mean (or average) of a data set, you add all the values together and then divide by the count of the values.

Firstly, for the mean without the outlier, we add 33+33+38+35+37+40 = 216, which we then divide by the 6 values, giving us 36. So, the mean without considering the outlier is 36.

For the mean considering all values including the outlier (57), calculate 33+33+38+35+57+37+40 = 273, then divide by the 7 values, which gives us approximately 39. The answer to the nearest tenth is 39.0. Therefore, the mean of this data set with the outlier is 39.0 and without the outlier is 36.0.

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If x is zero then you must replace x with zero and use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction) to solve

7 + (-4(0)^2)

7 + (-4(0))

7 + 0

7

If x is 0 then the expression equals 7

Hope this helped

~Just a girl in love with Shawn Mendes

Answer:

[tex]\boxed{7}[/tex]

X=0 is 7.

7 is the correct answer.

The answer should have a positive sign.

Step-by-step explanation:

Order of operations

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

from left to right.

Distributive property: a(b+c)=ab+ac

[tex]7+(-4x^2)[/tex]

[tex]7+-4x^2[/tex]

[tex]7-4*0^2[/tex]

Do exponent.

[tex]0^2=0*0=0[/tex]

[tex]7-0=7[/tex]

7 is the correct answer.

Hope this helps you!

Thanks!

Have a nice day! :)

-Charlie

Answer:7/20 = 0.35 = 35%=500x.35 =175 men

40%=.40x500 =200 women

200+170=370

500-370

125 children

Step-by-step explanation:

Answer:

There are 175 men, 200 women, and 125 children.

Step-by-step explanation:

7/20 = M/500; M = 175

0.4 x 500 = W; W = 200

175 + 200 + C = 500; C = 125

The Fahrenheit temperature range at which the antifreeze protects the car, converted from Celsius, is -40°F ≤ F ≤ 284°F.

To convert the Celsius range to a Fahrenheit range, you can use the conversion formula, F = (9/5)*C + 32. Using this formula, for -40°C the Fahrenheit equivalent would be F = (9/5)*(-40) + 32 which equals -40°F, and for 140°C the Fahrenheit equivalent would be F = (9/5)*(140) + 32 = 284°F. Therefore, the compound inequality representing the Fahrenheit temperature range at which the antifreeze protects the car is -40°F ≤ F ≤ 284°F.

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Answer:

3/4x + (7 × Q)

∆

|

That's an x not multiplication

Answer:

[tex]7q + \frac{3}{4}x[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}\text{Product of 7 and q} & = & 7q\\\\\text{Three-fourths of x} & = & \frac{3}{4}x \\\\\text{Three fourths of x added to product of 7 and q} & = & 7q + \frac{3}{4}x \\\\\end{array}[/tex]

For this case we must indicate an expression equivalent to:

[tex]x ^ {- \frac {5} {3}}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, we can rewrite the expression as:

[tex]\frac {1} {x ^ {\frac {5} {3}}}[/tex]

We also have that by definition of properties of powers it is fulfilled that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, the expression is like:

[tex]\frac {1} {\sqrt [3] {x ^ 5}}[/tex]

ANswer:

Option B

Answer:

The upper graph

Step-by-step explanation:

We have two quadratic function here

[tex]y=-x^{2} +3x+5\\y=x^{2} +2x\\[/tex]

If we perform the function f(x) + g(x), which is nothing more than the sum of the two functions, we obtain a linear function, since the quadratic terms are eliminated by themselves

[tex]5x+5[/tex]

Answer:

5 meters

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z -----> the scale factor

P1 -----> the perimeter of the reduced rectangle on the right

P2 ----> the perimeter of the original rectangle on the left

[tex]z=\frac{P1}{P2}[/tex]

substitute

[tex]z=\frac{24}{30}=0.8[/tex]

step 2

Find the width of the reduced rectangle on the right

[tex]P1=2(L+W)[/tex]

substitute the given values

we have

[tex]L=8\ m[/tex] ---> see the attached figure to better understand the problem

[tex]24=2(8+W)[/tex]

[tex]12=8+W[/tex]

[tex]W=4\ m[/tex]

step 3

Find the width of the original rectangle on the left

To find the width of the original rectangle on the left, divide the width of the reduced rectangle on the right by the scale factor

so

[tex]W=4/0.8=5\ m[/tex]

Answer:

A. 5 meters

Step-by-step explanation:

Step-by-step explanation:

Let's start with the y-intercept.  (0, 50) is shifted 10 units to the right and becomes (10, 50).  Next, we know the slope is 5.  We can use this to plot more points, or we can use it to write an equation in point-slope form:

y - 50 = 5 (x - 10)

y - 50 = 5x - 50

y = 5x

So the new y-intercept is (0, 0).

What this means is that Jeremy's savings account will be worth $50 in ten years.

If we compare the new y-intercept to the old one, we see that the 10 unit shift to the right is the same as a 50 unit shift down.  Shifting graph B up 50 units will bring us back to the original graph.

distance = √(x1 - x2)^2 + (y1 - y2)^2

distance = √(-6 + 1)^2 + (7 - 1)^2

              = √25 + 36

              = √61

To the nearest whole unit:

√61 = 8

So your answer is:

about 8 units

Answer:

About 8 units

Step-by-step explanation:

I got it right :)

Answer:

Option B

When it was purchased (year 0) the coin was worth $7

Step-by-step explanation:

we have

[tex]f(t)=7(2)^{t}[/tex]

This is a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

In this problem we have

a=$7

b=2

b=1+r

so

2=1+r

r=1

r=100%

The y-intercept is the value of the function when the value of x is equal to zero

In this problem

The y-intercept is the value of a rare coin when the year t is equal to zero

[tex]f(0)=7(2)^{0}[/tex]

[tex]f(0)=\$7[/tex]

therefore

The meaning of y-intercept is

When it was purchased (year 0) the coin was worth $7

Answer:

a) 4/11

b) 2/11

c) 1/11

d) 7/11

Answer:

[tex]\large\boxed{y-4=\dfrac{9}{2}(x+5)}\\\boxed{9x-2y=-53}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-7, -5) and (-5, 4).

Calculate the slope:

[tex]m=\dfrac{4-(-5)}{-5-(-7)}=\dfrac{9}{2}[/tex]

Put it and coordinates of the point (-5, 4) to the equation:

[tex]y-4=\dfrac{9}{2}(x-(-5))[/tex]

[tex]y-4=\dfrac{9}{2}(x+5)[/tex] → the point-slope form

Convert to the standard form Ax + By = C :

[tex]y-4=\dfrac{9}{2}(x+5)[/tex]         multiply both sides by 2

[tex]2y-8=9(x+5)[/tex]        use the distributive property

[tex]2y-8=9x+45[/tex]           add 8 to both sides

[tex]2y=9x+53[/tex]          subtract 9x from both sides

[tex]-9x+2y=53[/tex]           change the signs

[tex]9x-2y=-53[/tex] → the standard form

let's recall that there are 16oz in 1 lbs, so then 12lbs is 12*16 = 192oz, plus 5, that makes it 197oz, so then 12lb 5oz is really 197oz.

likewise, 7lb is 7*16 = 112oz, plus 10 that makes it 122oz.

197 - 122 = 75 oz

and 75 oz is just 16+16+16+16+11, 4lbs and 11 oz.

Answer:

$2,812.50

Step-by-step explanation:

Let

y ----> amount that Sarah earn this month

x ----> amount of sales over $5,750

we know that

5%=5/100=0.05

The linear equation that represent this situation is

y=4(525)+0.05(x)

Find the value of x

x=20,000-5750=$14,250

substitute

y=4(525)+0.05(14,250)=$2,812.50

Sarah Jones earned $9,725 this month.

Sarah Jones earns $525 per week selling life insurance for Farmer’s Insurance plus 5% of sales over $5,750. Sarah’s sales this month (four weeks) are $20,000. To find out how much Sarah earns this month, we need to calculate her base salary and her commission earned from sales over $5,750:

Therefore, Sarah earns $9,725 this month.

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[tex]\bf -2(bx-5)=16\implies bx-5=\cfrac{16}{-2}\implies bx-5=-8\implies bx=-8+5 \\\\\\ bx=-3\implies \boxed{x=\cfrac{-3}{b}} \\\\[-0.35em] ~\dotfill\\\\ b=3\qquad \qquad x=\cfrac{-3}{\underset{b}{3}}\implies \boxed{b=-1}[/tex]

180° - 113° - 53° = 14°

The answer is b. 14

Recall that

[tex]\cos2\theta=2\cos^2\theta-1[/tex]

and

[tex]\tan^2\theta+1=\sec^2\theta=\dfrac1{\cos^2\theta}[/tex]

Then

[tex]\cos2\theta=\dfrac2{\tan^2\theta+1}-1\implies\cos2\theta=\boxed{\dfrac7{25}}[/tex]

Answer:

[tex]cos2\theta=\frac{7}{25}[/tex]

Step-by-step explanation:

This is a question of Trigonometric Identities. In addition to this, In quadrant IV the cosine of the angle is naturally negative. This explains the negative value for [tex]tan\theta=-3/4[/tex]

The double angle formula

Let's choose a convenient identity, for the double angle [tex]cos2\theta[/tex]

[tex]\\tan \theta=-3/4 \\ cos2\theta =cos^{2}\theta -sen^{2}\theta\\cos2\theta =2cos^{2}\theta-1\\\\1+tan\theta^{2} =sec^{2}\theta\\\\ 1+(\frac{-3}{4})^{2} =\frac{1}{cos^2 \theta} \\\\\frac{25}{16}=\frac{1}{cos^{2}\theta}\\ cos^{2}\theta=\frac{16}{25}[/tex]

Finally, we can plug it in:

[tex]cos2\theta =2cos^{2}\theta -1\\cos2\theta =2\left ( \frac{16}{25} \right )-1 \Rightarrow cos2\theta=\frac{7}{25}[/tex]

Answer:

affect males more than females

can be carried by females, without being expressed

are caused by genes carried on the X and Y chromosomes

Step-by-step explanation:

Answer:

I and III only

Step-by-step explanation:

step 1

we know that

In this problem

A, B and C are collinear

so

A', B' and C' are collinear too

because the transformation is a translation

The translation does not modify the shape or length of the figure

AB=A'B'

AC=A'C'

BC=B'C'

step 2

The distance

AA'=BB'=CC'

because AB and A'B' are parallel

Answer:

[tex]V=312\pi\ mm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the volume of a semi-sphere plus the volume of the cone

so

[tex]V=\frac{4}{6}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]

we have

[tex]r=6\ mm[/tex]

[tex]h=14\ mm[/tex]

substitute

[tex]V=\frac{4}{6}\pi (6)^{3} +\frac{1}{3} \pi (6)^{2} (14)[/tex]

[tex]V=144\pi +168\pi[/tex]

[tex]V=312\pi\ mm^{3}[/tex]

Answer:

312 πmm^2

Step-by-step explanation:

On edg

Answer:

c=ab/(2b+a)

Step-by-step explanation:

20^c = 4^c  *  5^c

20^c=  (2^2)^c   * 5^c

20^c= (2 )^(2c)   * ( 5 )^c

Raise both sides to power a

20^(ca)=(2^a)^(2c)  * (5  )^(ac)

20^(ca)=(20^c)^(2c) * (5  )^(ac)

Raise both sides to power b

20^(cab)=(20)^(2c^2b)*(5^b)^(ac)

20^(cab)=20^(2c^2b) * (20^c)^(ac)

20^(cab)=20^(2c^2b) * 20^(ac^2)

Rewriting using law of exponents on right hand side

20^(cab)=20^(2c^2b+ac^2)

Now bases are same so that means the exponents have to be the same, that is we have:

cab=2c^2b+ac^2

assuming c is not 0, divide by c on both sides

ab=2cb+ac

Factor the right hand side

ab=c(2b+a)

Divide both sides by (2b+a)

c=ab/(2b+a)

C  is expressed in terms of b as c = [tex](5^b) / 2.[/tex]

To express c in terms of b in the equation [tex]2^a = 5^b = 20^c[/tex], we need to use the property of exponents that states:

[tex]a^(m * n) = (a^m)^n[/tex]

Let's first express [tex]20^c[/tex] in terms of 2 and 5:

[tex]20^c = (2^2 * 5)^c = 2^(2c) * 5^c[/tex]

Now, we have the equation:

[tex]2^a = 5^b = 2^(2c) * 5^c[/tex]

Since the bases (2) and (5) are equal, the exponents must also be equal:

a = 2c

Now, we can express c in terms of b:

Divide both sides of the equation by 2:

c = a/2

Since we know that a = [tex]5^b[/tex], we can substitute it into the equation:

[tex]c = (5^b) / 2[/tex]

So, c is expressed in terms of b as c = (5^b) / 2.

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Answer:

25h-35=440

440+35=25h

475=25h

475÷25=h

h=19

19 hours

It will take 19 hours of lessons.

An equation is formed of two equal expressions. The answer describes the correct solution for the situation It will take 19 hours of lessons. The correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Ahmet rents a piano for $35 per month. He earns $25 per hour giving piano lessons to students. Therefore, the profit earned by Ahmet will be,

Profit = Total Earning - Expenditure

Profit = Total Earning - Cost of renting the piano

Profit = $25x - $35

Where x represents the number of hours

Now, since Ahmet wants to earn a profit of $440, this month. Therefore, we can write,
$440 = $25x - $35

$440 + $35 = $25x

$475 = $25x

x = $475 / $25

x = 19

Thus, Ahmet needs to give 19 hours of lessons in order to earn $440 profit.

Hence, the answer describes the correct solution for the situation is It will take 19 hours of lessons.

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Answer:

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

Please let me know the choices to better help you.

Step-by-step explanation:

I see zeros at x=-2 , x=0 , x=1 , x=3.

Any time it makes like a little U or upside down U at a zero you are going to have a even power on your factor (for which the zero occurs).  If it goes through the zero increasing or decreasing (not making a kind of U shaped upside down or upside right), it is an odd power.

So at x=-2, (x+2) is going to have an odd power

So at x=0,  (x-0) or (x+0) or even just x is going to have a odd power

So at x=1,  (x-1) is going to have an odd power

So at x=3, (x-3) is going to have an even power

So the polynomial could be represented by

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

Answer:

option B. the square of the sum of 2 times x and 5

Step-by-step explanation:

we have

[tex](2x+5)^{2}[/tex]

we know that

The algebraic expression [tex](2x)[/tex] is equal to the phrase " Two times x" (the number two multiplied by x)

The algebraic expression [tex](2x+5)[/tex] is equal to the phrase " The sum of two times x and 5" (the number two multiplied by x plus the number 5)

The algebraic expression [tex](2x+5)^{2}[/tex] is equal to the phrase " The square of the sum of two times x and 5"

Answer:

B: 5^4

Step-by-step explanation:

however many of the same numbers is the little exponent

Exponent means exactly repeated multiplications of the same number: [tex]a^b[/tex] means that you have to multiply [tex]a[/tex] by itself [tex]b[/tex] times.

So, [tex]5\times5\times5\times5[/tex] means to multiply 5 by itself 4 times, which is written as [tex]5^4[/tex].