Solve for system of equations. y = x²-3x + 4
x + y = 4

Answer:

x = z - m + y

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z = m+x-y}[/tex]

To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.

[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]

Therefore, the answer to this question is x = z - m + y

Please let me know if you have any questions regarding my answer or explanation!

Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:

b. 0.2.

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

In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:

p = 26/130 = 0.2, which means that option b is correct.

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Answer:

C

Step-by-step explanation:

The balloon’s vertical distance above the ground is 721.7 f

In order to determine the balloon's vertical distance, we will use the SOH CAH TOA identity

Given the following parameters

Angle of depression = 30 degrees

Horizontal distance =1250 feet

Required

vertical distance H

Using the SOH CAH TOA identity

tan 30 = H/1250

H = 1250tan30
H = 721.7 feet

Hence the balloon’s vertical distance above the ground is 721.7 feet

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Answer:

721.7                                          

Step-by-step explanation:

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

If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

Tₙ = a + (n-1)d

(for all positive integer values of n)

Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,

4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........

Therefore,

Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,

a₃₆ = 4.54 + (36-1)4.54

a₃₆ = 163.44

Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

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Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:

[tex]y = a(3)^x[/tex]

Hence, after 2 hours:

[tex]y = a(3)^2 = 9a[/tex]

Which means that the multiplier is of 9.

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[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,7)\qquad R(8,-5)\qquad \qquad \stackrel{\textit{ratio from P to R}}{4:5} \\\\\\ \cfrac{P\underline{Q}}{\underline{Q} R} = \cfrac{4}{5}\implies \cfrac{P}{R} = \cfrac{4}{5}\implies 5P=4R\implies 5(-10,7)=4(8,-5)[/tex]

[tex](\stackrel{x}{-50}~~,~~ \stackrel{y}{35})=(\stackrel{x}{32}~~,~~ \stackrel{y}{-20})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-50 +32}}{4+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{35 -20}}{4+5} \right)} \\\\\\ Q=\left( \cfrac{-18}{9}~~,~~\cfrac{15}{9} \right)\implies Q=\left( -2~~,~~\cfrac{5}{3} \right)[/tex]

Answer:

the value of b to 2

The value of b changes to 2.

The correct option is C.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

We have,

Equation: h(x) = -x + 5

Now, using the slope intercept form

y = mx + b

From which we get

m = -1 and b=5

Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get

y = -x+5 -3

y = -x +2.

Here y-intercept is 2.

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The 3D prism that produced the cross-section of a triangle is a triangular prism.

From the given figure, we can see that the cross-section is a triangle

One of the faces of a triangular prism is a triangle.

This means that when the triangular prism is cut vertically, a triangle face is created

Hence, the 3D prism that produced the cross-section of a triangle is a triangular prism.

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Answer:

38.1971

Step-by-step explanation:

The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971

Answer:

0.0178 is the answer

The probability will include:

The probability of P(A and 1) will be:

= 1/4 × 1/6

= 1/24

The probability of P(C and 2) will be:

= 1/4 × 2/6

= 1/12

The probability of P(B and 3) will be:

= 2/4 × 1/6

= 1/12

The probability of P(A and 4) will be:

= 1/4 × 2/6

= 1/12

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The answer to the all parts given below.

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

For 5 cuts number of pieces will be 11 pieces.

General formula:

Tn= 2n+1

For 153 rope pieces number of rope cutting

2n+1=153

2n= 152

n= 76

For 11 cuttings rope pieces will be

2(11)+1

= 23

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Answer: 8.8

Step-by-step explanation:

Because [tex]\angle S \cong \angle S[/tex] by the reflexive property, we know that [tex]\triangle STU \sim \triangle SQR[/tex] by AA.

So, by the triangle proportionality theorem,

[tex]\frac{x}{5.3}=\frac{11.1}{6.7}\\x=(11.1/6.7)(5.3) \approx \boxed{8.8}[/tex]

The equation that could be used to determine the volume of Box B is (B = 14.325cm³ - 5.61cm³) and the volume of Box B is 8.715cm³.

This question is incomplete, the complete question is:

The sum of the volume of two rectangular prisms, box a and box b are 14.325cm cubed. Box a has a volume of 5.61cm.

a. Let B represent the volume of Box B in cubic centimeters. Write an equation that could be used to determine the volume of Box B.

b. Solve the equation to determine the volume of Box B

Volume is simply the amount of space that is enclosed within a container.

Given that;

a)

Let B represent the volume of Box B in cubic centimeters. The equation that could be used to determine the volume of Box B will be;

Sum of the volume of two rectangular prisms A&B = Volume of Box A + Volume of Box B

14.325cm³ = 5.61cm³ + B

B = 14.325cm³ - 5.61cm³

Hence, The equation that could be used to determine the volume of Box B is B = 14.325cm³ - 5.61cm³

b)

To determine the volume of Box B, we solve the equation.

B = 14.325cm³ - 5.61cm³

B = 8.715cm³

Hence, the volume of Box B is 8.715cm³.

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Answer:

y=2x-5

explanation

m is gradient so rise over run and b is the y intercept which is -5

Answer: y = 2x - 5

Step-by-step explanation:

Method I:

▪︎ Slope: m = (y2 - y1) / (x2 - x1)

▪︎ b is where the graph crosses the y-axis

▪︎ Points: (1, -3), (2, -1)

▪︎ m = (-1 - (-3)) / (2 - 1) = (3 - 1) / (1) = 2

▪︎ b = -5

▪︎ => y = 2x - 5

Method II:

▪︎ y = mx + b

▪︎ Points: (1, -3), (2, -1)

▪︎ System of equations:

-3 = m*1 + b,

-1 = m*2 + b

-3 = m + b,

-1 = 2m + b

m = -b - 3,

-1 = 2(-b - 3) + b

m = -b - 3,

-1 = -2b - 6 + b

m = -b - 3,

-1 + 6 = -2b + b

m = -b - 3,

5 = -b

m = -(-5) - 3,

b = -5

m = 2,

b = -5

▪︎ => y = 2x - 5

Answer:

Step-by-step explanation:

We can classify triangles by their sides into three types:

The length of the segment HI in the figure is 32.9

To do this, we make use of the following secant-tangent equation:

HI² = KI * JI

From the figure, we have:

KI = 21 + 24 = 45

JI = 24

So, we have:

HI² = 45 * 24

Evaluate the product

HI² = 1080

Take the square root of both sides

HI = 32.9

Hence, the length of the segment HI is 32.9

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Answer:

-2.6

Step-by-step explanation:

-1.4+(-1.2)

-1.4-1.2=-2.6

Hope this helps!

If not, I am sorry.

The value of y in the given logarithmic equation is 3. The correct option is C. 3

From the question, we are to determine the value of y in the given logarithmic equation

The given equation is

[tex]log_{4}64=y[/tex]

By applying one of the laws of logarithm, we get

[tex]64 = 4^{y}[/tex]

Now, express 64 in index form,

[tex]4^{3} = 4^{y}[/tex]

Since the bases are equal, we can equal the powers to get

3 = y

∴ y = 3

Hence, the value of y in the given logarithmic equation is 3. The correct option is C. 3

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Answer:

250.000$

Step-by-step explanation:

so you multiple 2.000 by 25

The amount of plywood that he needs to buy will be 21 square feet.

Let the prism with a length of L of the rectangular surface.

And the dimension of the triangle is A, B, and C. Then we have

SA = 2(area of triangle) + 3(area of rectangle surface)

A triangular prism.

The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.

The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.

Then the area of the triangle will be

⇒ 1/2 x 2 x 1.5

⇒ 1.5 square feet

The area of the rectangles will be

⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5

⇒ 18 square feet

Then the surface area of the triangular prism will be

Surface area = 2 x 1.5 + 18

Surface arae = 3 + 18

Surface area = 21 square feet

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t=2/61

1 Rearrange terms

2

Multiply the numbers

3

Combine like terms

4

Add

10

to both sides

5

Simplify

6

Add

303t

to both sides

7

Simplify

8

Divide both sides by the same factor

9

Simplify

Answer:

1

Step-by-step explanation:

let x be the number to be added to 5 and 3

expressing the ratios in fractional form

[tex]\frac{5+x}{3+x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3(3 + x) = 2(5 + x) ← distribute parenthesis on both sides

9 + 3x = 10 + 2x ( subtract 2x from both sides )

9 + x = 10 ( subtract 9 from both sides )

x = 1

then the number to be added to both is 1

Answer:

A=2, B=3, C=5

Step-by-step explanation:

Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way

[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]

Now, for the two polynomials to be the same we need to have, at the same time

[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]

You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.

Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.

[tex]\huge\sf\underline{Answer}[/tex]

Let's find out ~

Given :-

Solution :-

[tex]\sf\rightarrow \:LSA \: of \: cuboid \: = 2h \: ( \: l + b \: )[/tex]

[tex]\sf\rightarrow \: 180 = 2h \: (10 + 5)[/tex]

[tex]\sf\rightarrow180 = 2h \: \times 15[/tex]

[tex]\sf\rightarrow 180 = 30h \: [/tex]

[tex]\sf\rightarrow \: 30h \: = 180[/tex]

[tex]\sf\rightarrow \: h = \frac{180}{30} [/tex]

[tex]\sf\rightarrow \: 6[/tex]

Thus , the height of cuboid is 6m

The statement that can never be true is the data set contains a value of 3.

A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

minimum number = 8

maximum number = 22

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The approximate length of arc QR to nearest tenth is 9.9cm

The formula for calculating the length of an arc is expressed as:

L = r theta

where

r is the radius of an arc = 20cm/2 = 10cm

theta = 180 - 123 = 57 degrees

Determine the length of an arc

L = 10(57π/180)
L = 57π/18
L = 9.94cm

Hence the approximate length of arc QR to nearest tenth is 9.9cm

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Answer:

9.9

Step-by-step explanation:

Answer:

it would end up being about $40.73

Step-by-step explanation:

multiply 0.078 by 3 then multiply that by 33

Answer:

hope you can understand