Find the measure of

Answer: (0, 1), (-1, -3)

Given two equation's:

Solve them simultaneously:

[tex]\sf 2x^2 + 6x + 1 = -4x^2 + 1[/tex]

[tex]\sf 2x^2 + 4x^2 = 1 - 1[/tex]

[tex]\sf 6x^2 + 6x = 0[/tex]

[tex]\sf 6x(x + 1) = 0[/tex]

[tex]\sf 6x = 0, \ x + 1 = 0[/tex]

[tex]\sf x = 0, \ x = -1[/tex]

(a) When x = 0,     y = −4(0)² + 1 = 1

(b) When x = -1,    y = -4(-1)² + 1 = -3

Solution: (x, y) → (0, 1), (-1, -3)

Answer:

System of equations

[tex]\large \begin{cases}y=2x^2+6x+1\\y = -4x^2+1\end{cases}[/tex]

To solve the given system of equations, use the substitution method:

[tex]\large\begin{aligned}2x^2+6x+1 & = -4x^2+1\\2x^2+6x+1+4x^2-1 & = 0\\6x^2+6x & = 0 \\6x(x+1) & = 0\\\implies x+1 & = 0 \implies x=-1\\\implies 6x & = 0 \implies x=0\end{aligned}[/tex]

Therefore the x-values of the solutions are:

        [tex]\large \begin{aligned}x & =-1\\x & =0\end{aligned}[/tex]

Substitute the found values of x into the second equation to find the y-values:

[tex]\large \begin{aligned}x & =-1 & \implies &-4(-1)^2+1 =-3 & \implies & (-1,-3)\\x & =0 & \implies & -4(0)^2+1 =1 & \implies & (0,1)\end{aligned}[/tex]

Therefore, the solutions of the system of equations are:

(-1, -3) and (0, 1)

The equation is x² + 11x = 12. Here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have an area of border  48 square inches.

Menu dimensions without border =  13-inch by 9-inch

The area of the border can be expressed by the equation:

area of border = area of rectangle with border—area of rectangle without

                            border

48 = (13 + 2x)(9 + 2x) - 13×9

[tex]\rm 48=4x^2+44x[/tex]

After simplification:

[tex]\rm 4x^2+44x-48=0[/tex]

or

x² + 11x = 12

Find the solution of the above quadratic equation:

x = 1 or x = -12(width cannot be negative)

Width should be 1 inches.

We have given x = 2.5 it is not reasonable for the border to be 2.5 inches wide. Due to the cost of printing, the border should have an area of 48 square inches.

Thus, the equation is x² + 11x = 12 here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

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Answer:

1.B

2.A

3.B

4.(not sure)

5. C

Step-by-step explanation:

Give brainliest please!

Hope this helped :)

Answer:

B: A square is a quadrilateral

Step-by-step explanation:

Considering that 12 is a root of the function, the value of coefficient Q is of 12.

It means that f(x) = 0.

In this problem, the function is given by:

f(x) = x² - 13x + q.

Since 12 is a root, we have that f(12) = 0, hence:

12² - 13 x 12 + q = 0

q - 12 = 0.

q = 12.

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The system of linear equations that best represents the situation are:

z+y=18

3z +2y=44

In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.

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Answer:

7

Step-by-step explanation:

m=pendiente

por lo tanto:

pendiente=7

Hii!

__________________________________________________________

Answer:

Slope = 7! ^^

Step-by-step explanation:

Note that the equation is given to us in slope intercept form.

The slope intercept formula is y=mx+c.

m denotes the slope

c denotes the y intercept.

/--------------\

The slope of the line that we are working with is 7.

Remember how I said that the slope of the line y=mx+c is m?

Similarly, the slope of the line y=7x-3 is 7! ^^

--

Hope that this helped! Best wishes.

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The value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

Evan has a bag of apples that weighs 3.545 pounds.

The value of the digit 5 in the tenths place of 3.545 is 0.500

The value of the digit 5 in the thousandths place of 3.545 is  0.005

Take the ratio of both values:

tenths place value/thousandths place value =  0.500/0.005

tenths place value/thousandths place value =  100

tenths place value = 100(thousandths place value)

Thus, the value of the digit 5 in the tenths place of 3.545 is 100 times the value of the digit 5 in the thousandths place.

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The ratio of any side and hypotenuse is always less than 1.

The question seems incomplete

The options are not given the options are

a. 1

b. 0.5

c. 2

[tex]sin\theta=\frac{Opposite side}{hypotenuse}[/tex]

Therefore, the ratio of any side and hypotenuse is always less than 1. Now, in the case of 0 or 90 degrees, the figure is no longer a triangle because one of the sides ceases to exist while the other side coincides with the hypotenuse.

This is the reason that in these extreme cases, sin and cosine take values 0 or 1.

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Answer:

B

Step-by-step explanation:

the symbol in the x < 0 has a line under it meaning it is a closed circle, and the other equation does not, so it is an open circle. And since the question has (or) in it, it means that the arrows should be facing away from eachother.

Answer: ~96.83°

Step-by-step explanation:

1) It's obvious that the largest angle is the opposite to the largest side.

▪︎ QR = 18 (the largest side)

=> <QPR is the largest angle

2) Cosine Rule:

▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)

▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)

▪︎ 324 = 169 + 121 - 286*cos(QPR)

▪︎ 34 = -286*cos(QPR)

▪︎ cos(QPR) = -34/286

▪︎ <QPR = arccos(-34/286) = 96.827...°

Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

x = 29.44

Step-by-step explanation:

[tex]tan31^{o} =\frac{x}{49}[/tex]

[tex]x=49tan31^{o}[/tex]

[tex]x=29.44[/tex]

Hope this helps

Answer:

Domain = [0 , +∞)

Step-by-step explanation:

since r is the radius of a circle

Then

r must be a positive number.

Then

r ≥ 0

NOTE : if r = 0 ,then the circle reduces to a point .

The quotient of the expression [tex]\frac{3y+2}{3y} divided \frac{6y^{2} + 4y}{3y + 2}[/tex]  is 3y + 2 / 6y

The quotient of the expression can be found as follows:

3y + 2 / 3y ÷ 6y² + 4y / 3y + 2

Therefore,

3y + 2 / 3y × 3y + 2 / 6y² + 4y

Hence,

3y + 2 / 3y × 3y + 2 / 2y(3y + 2)

Therefore,

1 / 3y × 3y + 2 / 2

Hence,

3y + 2 / 2(3y)

3y + 2 / 6y

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Answer:

Hey!

Your Answer Is,

No Triangles: A, C

One Triangle, F, D

Many Triangles: B,E

I hope this helps you!

Step-by-step explanation:

See below for the proof that ∠1 and ∠14 are supplementary angles

The attached diagram represents the missing information in the question.

The given parameters are:

The next step in the proof is as follows:

∠2 and ∠14 are corresponding angles.

This means that:

∠2 = ∠14

Recall that:

∠1 and ∠2 are supplementary angles

This means that:

∠1 + ∠2 = 180

Substitute ∠2 = ∠14

∠1 + ∠14 = 180

Supplementary angles add up to 180

Hence, ∠1 and ∠14 are supplementary angles

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Answer:

Step-by-step explanation:

the answer is D

The volume of each individual brick is 72 cubic inches.

The volume of a rectangular prism of height H, width W, and length L is given by:

V = L*H*W

In this case we have:

Then, replacing these in the volume equation, we get:

V = (8 in)*(4 in)*(2.25 in) = 72in³

So the correct option is the second one.

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Answer:

The volume of each individual brick is 72 cubic inches.

Step-by-step explanation:

How to get the volume of each brick?

The volume of a rectangular prism of height H, width W, and length L is given by:

V = L*H*W

In this case we have:

L = 8in

W = 4in

H = 2.25 in

Then, replacing these in the volume equation, we get:

V = (8 in)*(4 in)*(2.25 in) = 72in³

So the correct option is the second one.

#a

[tex]\\ \rm\Rrightarrow f(-4)[/tex]

[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]

[tex]\\ \rm\Rrightarrow -12+2[/tex]

[tex]\\ \rm\Rrightarrow -10[/tex]

#b

#1

[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]

Find y

[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]

Inverse is

[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]

#2

[tex]\\ \rm\Rrightarrow gof(x)[/tex]

[tex]\\ \rm\Rrightarrow g(f(x))[/tex]

[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]

If we factor out

[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]

[tex]\\ \rm\Rrightarrow 2x+1[/tex]

#c

[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]

[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]

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

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

[tex]\\ \rm\Rrightarrow 7x=-7[/tex]

[tex]\\ \rm\Rrightarrow x=-1[/tex]

Answer:

Given functions:

[tex]f(x)=3x+2[/tex]

[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]

Part (a)

[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]

Part (b)(i)

[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]

Part (b)(ii)

[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]

Answer:

[tex]\huge\boxed{\sf |AB|=10 \ units}[/tex]

Step-by-step explanation:

Coordinate of A = [tex](x_1,y_1)[/tex] = (-7,-6)

Coordinate of B = [tex](x_2,y_2)[/tex] = (1,0)

We will use distance formula to find the length of AB.

[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\|AB|=\sqrt{(1-(-7))^2+(0-(-6))^2} \\\\|AB|=\sqrt{(1+7)^2+(6)^2} \\\\|AB|=\sqrt{(8)^2+36} \\\\|AB|=\sqrt{64+36} \\\\|AB|=\sqrt{100} \\\\\boxed{|AB|=10 \ units}\\\\\rule[225]{225}{2}[/tex]

The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.

A triangle is a shape that has three sides. The sides can be measured using a ruler.

The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.

Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.

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Answer:

a

Step-by-step explanation:

Using it's concept, it is found that the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:

[tex]p = (0.25)^{100}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 25% of the adults own a landline, and the probabilities for each adult are independent, hence the probability that everyone in a simple random sample of 100 young adults owns a landline is given by:

[tex]p = (0.25)^{100}[/tex]

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[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]

Answer:

the answer=  -5

Answer: 13.7 ft

Step-by-step explanation:

Use Pythagorean theory to find radius

C^2 - B^2 = A^2

We know the hypotenuse (cone to edge) is 15

We will call that C

We know the height is 6

We will call that B

We are looking for A or radius

15^2 - 6^2 = A^2

225 - 36 = A^2

189 = A^2

Take square root of both sides

13.7 = A (radius)

taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2.  Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).

[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill[/tex]

Check the picture below.

Answer:

Your answer is 3282.34

Step-by-step explanation:

1/3 x 3.14 x 14 ^2 x 16

this is all you have to do really.

Answer:

B. -113 inches

Step-by-step explanation:

First you have to find the radius of the two pizzas. The radius is half of the diameter. So, the first pizza would have a radius of 8 inches, since 8 is half of 16. The second pizza would have a radius of 10 inches, since 10 is half of 20. Then you would use the area formula to find the area of the two pizzas. The area formula is A=3.14R^2. The area of the first pizza is 201.06. The area of the second pizza is 314.16. Then you subtract those two numbers to get -113.1. The answer is -113 inches.

Answer:

g= 6.5

Step-by-step explanation:

O.25(g+1.5) = 2

(g+1.5) = 2/0.25 divide both sides with 0.25

g+1.5 = 8

g = 8-1.5

g = 6.5

The equation that can be used to find the exponential decay is 3000 = 4599e^k.

The lawn mower is decreasing in value, thus it is the decay constant that would be found.

The formula that can be used to find the value of an asset that decays exponentially is:

Future value = present value x (e^k)

3000 = 4599e^k.

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