which statements are true? select each correct answer.
a) 30a^6-24a^2=3à^2(10a^4-8)
b) 24a^4+18=6(4a^⁴+3)
c) 16a^5-20a^3=4a^3(4a^2-5)
D) 12a^3+8a=4(3a^3+2a)​

Answer:

x = 12 and y = 0

Step-by-step explanation:

Use elimination by adding the equations together.

-2x + 15y =-24

2x + 9y =  24

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

24y = 0

y=0

Then substitute y = 0 into one equation to find x.

-2x + 15(0) = -24

-2x + 0 = -24

-2x = -24

x = 12

Answer: x = 12 y = 0

Step-by-step explanation:

Answer:

Look at the picture

Step-by-step explanation:

[tex]\log_ab=c\iff a^c=b\\\\\text{Therefore}\\\\f(x)=b^x\to y=b^x\\\\\text{find}\ f^{-1}(x).\ \text{Exchange}\ x\ \text{and}\ y\ \text{and solve for}\ y:\\\\b^y=x\qquad\text{logarithm iwth base b of both sides}\\\\\log_bb^y=\log_b(x)\qquad\text{use}\ \log_ab^m=m\log_ab\\\\y\log_bb=\log_b(x)\qquad\text{use}\ \log_aa=1\\\\y=\log_b(x)\\\\f^{-1}(x)=\log_b(x)\to g(x)=f^{-1}(x)\\\\\text{Then:}\ f(a)=b\to g(b)=a[/tex]

Answer:

see explanation

Step-by-step explanation:

Factorise the numerators on both fractions

a² + 10a + 25 = (a + 5)(a + 5) ← perfect square

a² - 25 = (a - 5 )(a + 5) ← difference of squares

To divide, leave the first fraction, change division to multiplication and turn the second fraction upside down.

Hence

= [tex]\frac{(a+5)(a+5)}{a+5}[/tex] × [tex]\frac{a-5}{(a-5)(a+5)}[/tex]

Cancel both the (a + 5) factors on the numerator/ denominators and the (a - 5) factor on the numerator/denominator, leaving

= 1 ← as required

Answer: The correct answer is B. 5.97 feet

Step-by-step explanation:

Formula⇒A=π r2

* Hopefully the work helps:) Mark me the brainliest;)!!!

Answer:

5.97 feet

Step-by-step explanation:

Set up your equation as 112.07 = Pi*r^2

To simplify, divide 112.07 by Pi or an approximation of it and then find the square root of your answer.

112.07 = Pi*r^2

112.07/Pi = r^2

(112.07/Pi)^0.5=r

Answer:

There is no question

Step-by-step explanation:

Answer:

Im gonna guess and say it is answer 3.

Step-by-step explanation:

A rotation doesn't change the length of anything.

The length of the rotated line segment would be the same as the original line segment.

Because both Y values are the same, you just need to calculate the length of the X values.

5 to 0 = 5

0 to -6 = 6

Total length = 5 +6 = 11 units long.

Answer:

So option B is the correct answer .

Step-by-step explanation:

Since it is the multiplication of 1 X 3 matrix to 3 X 3 order matrix,

so the resultant product should be 1 X 3 because when we multiply two matrices it is the condition that if A is of order p X q and B is of order q X r,

the product matrix (suppose C ) will be of order p X r.

so the product will be

= [-1*3+2*2+4*0   -1*6+2*4+4*6   -1*1+2*0+4*2]

= [ 1      26     7] .

Answer:

36°

Step-by-step explanation:

∠A + ∠B + ∠C = 180°

∠A:∠B:∠C = 8:10:12 = 8x:10x:12x

8x + 10x + 12x = 180

                20x = 180

                    x =     9

∠A =   8x =  8 × 9 =  72°

∠B = 10x = 10 × 9 =  90°

∠C = 12x = 12 × 9 = 108°

∠C - ∠A = 108 -72 = 36 °

The difference between the largest and the smallest angle is 36°.

Answer:

Part a) [tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]

Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure.(the scale factor is greater than 1)

Part c) The scale factor is [tex]3[/tex]

Step-by-step explanation:

Part a) Write the similarity statement

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

[tex]\frac{AB}{A'B'}=\frac{BC}{B'C'} =\frac{AC}{A'C'}[/tex]

substitute the values

[tex]\frac{9}{27}=\frac{12}{36} =\frac{15}{45'}[/tex]

[tex]\frac{1}{3}=\frac{1}{3} =\frac{1}{3'}[/tex] ----> is true

therefore

the figures are similar

Part b) The dilation is an enlargement, because the corresponding sides of the image are larger than the corresponding sides of the original figure. (the scale factor is greater than 1)

Part c) we know that

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

Let

z------> the scale factor

x-----> corresponding side of the image

y------> corresponding side of the original figure

so

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

we have

[tex]x=A'B'=27\ units[/tex]

[tex]y=AB=9\ units[/tex]

substitute

[tex]z=\frac{27}{9}=3[/tex]

The scale factor is greater than 1

therefore

Is an enlargement

Answer:(A) ab/a’b’=bc/b’c’=ac/a’c’ (B) Figure a’b’c’ is an enlargement because it increase it’s sides larger than 1. (C) So we have to divide to get the scale factor for both of these figures 18/6=3 then you found the scale factor 3.

Step-by-step explanation:

The measure of Angle 1 is 35 degrees and the measure of Angle 2 is 55 degrees.

When two angles are complementary, their measures add up to 90 degrees. Let's define these two angles as follows: Angle 1 = x and Angle 2 = 2x - 15 (since it is 15 degrees less than twice the measure of Angle 1). You set up an equation based on the fact that the two angles add up to 90 degrees: x + 2x - 15 = 90. Solving this equation, you get 3x = 105, so x = 35. Thus, Angle 1 = 35° and Angle 2 = 2(35) - 15 = 55°.

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Answer:

[tex]7\frac{5}{7}\ laps[/tex]

Step-by-step explanation:

we know that

To find out how many laps they ran, divide the total distance by the distance of one lap

step 1

Convert the total distance from mixed number to an improper fraction

[tex]6\frac{3}{4}\ mi=\frac{6*4+3}{4}=\frac{27}{4}\ mi[/tex]

step 2

Find the number of laps

[tex]\frac{(27/4)}{(7/8)}=\frac{54}{7}\ laps[/tex]

step 3

Convert the number of laps to mixed number

[tex]\frac{54}{7}=\frac{49}{7}+\frac{5}{7}=7\frac{5}{7}\ laps[/tex]

The solution is

x = 27 and y = 43

See the image

The unit price of one pencil is $0.60.

The cost of one pencil (the unit price) can be found by dividing the total cost by the number of pencils. In this case, we have $3.60 divided by 6. This gives us a unit price of $0.60 per pencil.

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ANSWER

f(x) is an odd function.

EXPLANATION

The given function is symmetric with respect to the origin.

Hence it is an odd function.

We can also see from the graph that,

[tex]f(1) = 2[/tex]

and

[tex]f( - 1) = - 2[/tex]

This implies that,

[tex]f( - 1) = - f(1)[/tex]

Since

[tex]f( - x) = - f(x)[/tex]

the function is odd.

The correct answer is A.

Answer:

its b

Step-by-step explanation:

Answer:

2 × pi or (π) × 15 = 30 cm

Step-by-step explanation:

Answer:

The measure of the arc KW is [tex]160\°[/tex]

Step-by-step explanation:

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<A=\frac{1}{2}(arc\ KE+arc\ EW)[/tex]

substitute the values and solve for x

[tex](x+45)\°=\frac{1}{2}(x+20+3x)\°[/tex]

[tex](2x+90)\°=(4x+20)\°[/tex]

[tex]4x-2x=90\°-20\°[/tex]

[tex]2x=70\°[/tex]

[tex]x=70\°/2=35\°[/tex]

Find the measure of the arc KW

[tex]arc\ KW=(arc\ KE+arc\ EW)=(4x+20)\°[/tex]

substitute the value of x

[tex]arc\ KW=4(35\°)+20\°=160\°[/tex]

Answer:

Here is the following answers I got.

Step-by-step explanation:

(70/3)

23.3333

23 1/3

Answer:

2 hours per day

Step-by-step explanation:

19.5 - 5.5 = 14

14 / 7 = 2 hours per day

Mary needs to rehearse 2 hours per day for the next 7 days to meet her total rehearsal goal.

To calculate the total rehearsal time for Mary:

She has rehearsed for 5.5 hours.

She wants to rehearse a total of 19.5 hours.

Therefore, 19.5 - 5.5 = 14 hours

She needs to rehearse an additional 14 hours in the upcoming week.

To find out how many hours Mary must rehearse per day in the next 7 days:

14 / 7 = 2 hours/day

Answer:

22, 17, and 44.

Step-by-step explanation:

So what you do is you will have three equations that we will put together.

1. x. The first number is x because they don't give us anything about it.

2. x-5. It says that the second number is 5 less than the first number.

3. 2x. It says that the third number is 2 times the first number.

x+x-5+2x=83.

4x-5=83.

4x=88.

x=22.

That is the first number. To find the second and third, you will plug 22 into the x.

2. 22-5=17.

3. 2(22)=44.

22, 17, 44 are your answers.

Final answer:

By setting up equations based on the information provided, we solved for x as the first number and then used it to determine the other two numbers. The three numbers are 22, 17, and 44.

Explanation:

The sum of three numbers is 83. This is the first equation we'll use to solve the problem. Let's denote the first number as x. According to the question, the second number is 5 less than the first, which gives us the second equation y = x - 5. For the third number, it is given as 2 times the first, hence the third equation is z = 2x.

Now, we'll combine all three equations to express the sum:

x + (x - 5) + 2x = 83

Simplifying, we combine like terms:

4x - 5 = 83

Adding 5 to both sides gives us:

4x = 88

Dividing by 4, we find the first number:

x = 22

Now we'll use x to find the other two numbers:

y = 22 - 5 = 17

z = 2 × 22 = 44

Therefore, the three numbers are 22, 17, and 44.

Answer:

It would roughly be 7 inches and 1/5 of an inch.

I hope this answer helped you! If you have any further questions or concerns, feel free to ask! :)

Step-by-step explanation:

Two creek crossings are separated by distance A = 7.2 inches on the map.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

The information is ,

Let's say the equation looks like this: A

Right now, A is valued at

The two stream crossings' separation is indicated on the map as A.

And on the chart, 3 inches equals 0.75 miles, therefore the distance between the two stream crossings is 1.8 miles.

hence, 3 / 0.75 inches Equals 1 mile.

In the map, 1 mile equals 4 inches after simplifying the calculation.

The two creek crossing's distance on the map is therefore equal to 1.8 x 4.

The two stream crossings will be separated by 7.2 inches on map A.

Hence, the distance on the map is 7.2 inches.

Click here to learn more about equations.

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Answer:

Step-by-step explanation:

Only first one

P(both green) : [tex]\frac{1}{16}[/tex], P(both blue) : [tex]\frac{1}{4}[/tex], P(first orange and then blue) : [tex]\frac{1}{8}[/tex]

These probabilities are correct.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

According to the question

Louis spins the spinner twice.

Total number of favorable outcomes = {OB, OO, OB,OG, BB, BO, BB, BG, GG, GB, GO, GB, BB, BO, BB, BG} = 16

P(both green) :

Number of favorable outcomes = 1

P(both green) = [tex]\frac{1}{16}[/tex]

It is applicable.

P(both blue) :

Number of favorable outcomes = 4

P(both blue) = [tex]\frac{4}{16}[/tex] = [tex]\frac{1}{4}[/tex]

It is applicable.

P(first green and then blue) :

Number of favorable outcomes = 1

P(first green and then blue) =  [tex]\frac{1}{16}[/tex]

P(first orange and then blue) :

Number of favorable outcomes = 2

P(first orange and then blue) =  [tex]\frac{2}{16}=\frac{1}{8}[/tex]

It is applicable.

P(first orange and then green) :

Number of favorable outcomes = 1

P(first orange and then green) =  [tex]\frac{1}{16}[/tex]

Hence,

P(both green) : [tex]\frac{1}{16}[/tex], P(both blue) : [tex]\frac{1}{4}[/tex], P(first orange and then blue) : [tex]\frac{1}{8}[/tex]

These probabilities are correct.

Find out more information about probability here

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The answer is :

(x+5)(x+3)

Answer:

Part 1) The radius of the circle is [tex]17\ units[/tex]

Part 2) The points (15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

Part 1

we know that

The distance between the center of the circle at point (-7,-1) and the point (8,7) is equal to the radius of the circle

so

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

substitute the values

[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]

[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]

[tex]r=\sqrt{289}}[/tex]

[tex]r=17\ units[/tex]

Part 2

we know that

If the point (-15,y) lies on the circle, then the ordered pair must be satisfy the equation of the circle

The equation of the circle is equal to

[tex](x+7)^{2}+(y+1)^{2}=17^{2}[/tex] -----> equation of the circle in center radius form

substitute the value of x=-15 in the equation and solve for y

[tex](-15+7)^{2}+(y+1)^{2}=289[/tex]

[tex]64+(y+1)^{2}=289[/tex]

[tex](y+1)^{2}=289-64[/tex]

[tex](y+1)^{2}=225[/tex]

[tex]y+1=(+/-)15[/tex]

[tex]y=-1(+/-)15[/tex]

so

[tex]y=14[/tex]

[tex]y=-16[/tex]

therefore

The points (15,14) and (-15,-16) lies on this circle

see the attached figure to better understand the problem

Answer:

Part 1) The radius of the circle is  

Part 2) The points (15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

Answer:

Diameter = 50 cm

Step-by-step explanation:

We are given that the area of a home bakes pizza is [tex] 6 2 5 \pi cm ^ 2[/tex].

Here, we are assuming that the pizza is circular and we know that the area of a circle is given by: [tex]\pi r^2[/tex]

So equating the given value to find the value of the diameter.

[tex]\pi r^2[/tex] [tex]=625\pi[/tex]

[tex]r^2=625[/tex]

[tex]r=\sqrt{625}[/tex]

[tex]r=25[/tex]

If the radius is 25 cm, then  diameter = 25 × 2 = 50 cm

Answer:

The diameter of the pizza= 50 cm

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r is the radius of circle

It is given that, area of pizza is 625π cm²

A pizza is like a circle.

Find the radius of pizza

Area = πr²= 625π cm²

r² = 625π/π = 625

r = √625 = ±25

radius r = 25cm

To find the diameter of pizza

Diameter = 2r  = 2 * 25 = 50 cm

Answer:

Meters

Step-by-step explanation:

Because centimeters are to small to be a reasonable measurement for a car so you would have to use meters

Circumference= [tex]2\pi r[/tex]

If the diameter is 6 the radius will be 3

[tex]2\pi (3)[/tex]

Circumference= 18.85

Hey there!

The formula for circumference is πd, where d is diameter.

We are given that the diameter is 6, so the circumference is 6π.

However, we are asked for the approximate circumference, not the exact.

So, let's use 3.14 as π and simplify.

6 x 3.14 = 18.84

The approximate circumference of a circle with the diameter of 6 is 18.84.

Hope this helps!

Answer:

y = -4x - 38

Step-by-step explanation:

Parallel lines are parallel because they never intersect. As such, they have the same slope. The slope of the line y = -4x + 1 is -4. Substitute m = -4 and the point (-9,-2) into the point slope form of a line.

[tex]y -y_1 = m(x-x_1)\\y --2 = -4(x --9)\\y + 2 = -4(x+9)\\[/tex]

Apply the distributive property to find the slope intercept form.

y + 2 = -4(x+9)

y + 2 = -4x - 36

y = -4x - 38