III. Write each quadratic equation in standard form

1. 3x-2x² = 7

2.5-2x² = 6x

3.(x+3)(x+4)=0

4.(2x + 7)(x-1)=0

5,2x(x-3) = 15
ax²+bx+c=0

Answer:

They all come out to be infinity

Answer:

I can use the given (algebraic expression) 24c+12 to find the total cost of the order

The expression has two (terms). They are 24c and 12

In 24c the number 24 is the (coefficient) and the letter c is the (variable).

The term 24c represents a (product)

To find the total cost of the order I can (evaluate) the given expression

I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression

24c+12

24(6)+12

144+12

156

The total cost is 156

Hope this helps :)

The equation can be given as X+20 = 60

Wyatt needs to save $40 to buy the new game.

What is an equation?

An equation is an expression which has an equality symbol in it.

We are given that, Wyatt is saving up money for a new game. It costs $60,

including tax.

He has already saved $20. At least how much more money, X, does he need to save

Hence the equation can be given as

X + 20 = 60

On solving the equation X = 40

Hence Wyatt needs to save $40 to buy the new game

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The height of the poster is 20 inches.

The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.

The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".

30 = k*6

k = 30/6

k = 5

Hence, the poster is scaled up by a factor of five.

H = k*4

H = 5*4

H = 20

Hence, the height of the scaled-up poster is 20 inches.

The complete question is given below.

Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?

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Answer:

357 national parks

Step-by-step explanation:

420x85/100

420x17/20

21x17=

357

Answer: 67

Step-by-step explanation:

do the math

Answer: 27 dogs

Step-by-step explanation: 2 cats + 3 dogs= 5 in total for animals. 2/5x45=18 cats

3/5x45= 27 dogs

27+18=45 animals

There is 27 dogs in the shelter

Answer:

The parent graph has been dilated by a scale factor of 100 and has been moved to the right by 5 units

Step-by-step explanation:

The change made to f(x) = 1/x to f(x) = 100/x is a dilation by a scale factor of 100(the function has been multiplied by 100) .

The transformation of function f(x) = 100/x to f(x) = 100/x-5 is moving o the right 5 units (whenever a constant, let's call it "c", is being subtracted from the x when graphing, it means the graph has moved "c" units to the right, and vice versa--if "c" was added to x, then the graph would be moved "c" units to the left.).

TL;DR: f(x-c) means c units to the right, f(x+c) means c units to the left. f(x)*c means a dilation of c units.

The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]

Calculation

from ( - 3, 2) and (5, 7)

slope(m)  = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

[tex]=\frac{7 - 2}{5 - (-3)}[/tex]

[tex]= \frac{5}{8}[/tex]

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]

⇒[tex]2 = \frac{15}{8} + b[/tex]

⇒[tex]2 - \frac{15}{8} = b[/tex]

⇒[tex]\frac{16+15}{8} = b[/tex]

⇒[tex]\frac{31}{8} = b[/tex]

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]

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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.

When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,

Slope-intercept form

Point slope form

Two-point form

Intercept form

from ( - 3, 2) and (5, 7)

slope(m)  = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]

=7-(-2)/5-(-3)

=5/8

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , 2=5/8*(-3)+b

⇒2=15/8+b

⇒2-15/8=b

⇒16+15/8

31/8=b

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒y=5/8x +31/8

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The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.

Given that,

In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.

Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)

16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)

(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8

8 * Raina's velocity = 24

Raina's velocity = 3 kilometers per hour

As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.

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The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)

From the question, we have the following inequality that can be used in our computation:

5x + 3y > 12

Solving further, we need to collect the like terms

So, the expression becomes

3y > 12 - 5x

Next, we divide through the inequality by 3

So, we have the following representation

y > 12/3 - 5/3x

Evaluate

The equation becomes

y > 4 - 5/3x

At this point, we assume any value for x and then solve for y

Assume that the value of x is 3

So, we have the following representation

y > 4 - 5/3 * 3

Evaluate the products

y > -1

A value greater than -1 is 0

So, we have

x = 3 and y = 0

Express as ordered pairs

(x, y) = (3, 0)

Hence, the ordered pair of the solution is (3, 0)

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1. No This survey does not mean that cell phones are good for your health.

2. The factor that can be used as the best explanation for the strong correlation would be the general economic conditions of the people.

When one variable's value rises, the other variable's value also rises in a similar way. For instance, a student's exam score tends to be greater the more hours they study. Exam results and study time have a significant positive link.

A strong correlation, also known as a high correlation, indicates that two or more variables have a significant relationship with one another, whereas a weak or low correlation indicates that the variables are rarely associated.

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complete question

A survey of the world's nations in 2004 shows a strong positive correlation (hence, a positive association) between percentage of the country using cell phones and life expectancy in years at birth.

a. Does this mean that cell phones are good for your health? select one: ____ yes ____ no

b. What might best explain the strong correlation (as a lurking variable)?

Select one:

_____ Percent of young people

____ General economic conditions of the country

____ Percent of pop. living in cities

Step-by-step explanation:

the slow of a line is the factor of x in a "y = ..." firm of equation.

the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).

(B) and (C) are out, because there is no line with slope 3 (only -3).

the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).

(A) is out, as there is no line with the slope -2 (only +2).

so, (D) is the correct answer.

m= (6- 3)/ (-5 -1)

2x - y + 11= 0

The height of the tower is 87.4870 feet

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The body of the calculation is contained in the attached file.

In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet

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A) The matrix equation that represents the given information is;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) The cost of a banana is; $0.05

The cost of an orange is; $0.12

A matrix equation is defined as an equation where a variable stands for a matrix .

Let x represent cost of oranges

Let y represent cost of bananas

5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas

cost me $1.41. Thus, the equations are;

5x + 14y = 1.30  ----(1)

8x + 9y = 1.41   -----(2)

A) Now, the matrix form of the simultaneous equation above will be;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) Multiply the first equation by 8 and the second one by 5 to get;

40x + 112y = 10.4

40x +   45y = 7.05   Subtract to get;

            67y = 3.35

Divide both sides by 67 to get;

y = $0.05 per banana

Plug in 0.05 for y into eq 1 to get;

5x + 14(0.05) = 1.30

5x + 0.7 = 1.3

5x = 1.3 - 0.7

5x = 0.6

x = 0.6/5

x = $0.12

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Answer:

b

Step-by-step explanation:

the right side base angle and 80° are vertically opposite angles and are congruent, both 80°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

123° is an exterior angle of the triangle , then

x + 80 = 123 ( subtract 80 from both sides )

x = 43

The three valid congruency statements are; Triangle PQR = Triangle STU

Angles who are of same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of same measure, then

[tex]m\angle A = m\angle B[/tex] is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

Congruence statement states that a statement used in geometry that simply says that two objects are congruent, or has the  same shape and size.

Also, we can make congruence statements in words or in symbols. Using symbols we use the congruence symbol i,e  ≅ to indicate that two objects are congruent.

In the given triangles;

Angle T = Angle Q

QR = ST

TU = PQ

Triangle PQR = Triangle STU reason=ASA

Therefore, the three valid congruency statements are;

Triangle PQR = Triangle STU

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The angle which corresponds with angle 2 given that; lines m and n are parallel and are intersected by transversal p is; angle 6.

Corresponding angles by definition are any pair of angles each of which happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.

Therefore, it follows from the definition above that the angle which is corresponding to Angle 2 as required in the task content is; angle 6.

This follows from the fact that angles 2 and 6; each happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.

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The total number of completions Trevor  be expected to make is 25.

For the given question.

Let the number of completion by Trevor be 'x'.

Trevor completes 5 out of 8 passes.

Total passes are 40

Then, proportions set up is-

5/8 = x/40

x = 25

Thus, the total number of completions Trevor be expected to make is 25.

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

The function shown in the graph above is a discontinuous function, at x = -2

For values of x less than -2, the left side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - 1(x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2[/tex]

For values of x greater than -2, the right side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2[/tex]

So, the correct choice will be Option " A "

Answer:

[tex]\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

Step-by-step explanation:

When graphing piece-wise functions:

From inspection of the given graph:

Therefore, the definition of the function is:

[tex]\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

where a is some constant.

The only answer option that matches the given parameters is option A.

The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA

Given original diameter do = 12 mm

Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²

Deformed diameter d =10mm

Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²

Degree of cold work %CW = (Ao - Ad/Ao)X 100

                                             =(113. 097 - 78. 54/113.097) x 100

                                             = 30.56%

% CW is 30.56 %

Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.

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Answer:

57

Step-by-step explanation:

Straight line is 180 degrees

x+2x+9=180

3x=171

x=171/3

x=57

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The probability that the sum of the dice is 9 is, 4/33.

What is dice?

Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.

Let two fair dice are rolled.

So the possible number of outcomes are,

(1, 1)  (1, 2)  (1, 3)  (1, 4)  (1, 5)  (1, 6)

(2, 1)  (2, 2)  (2, 3)  (2, 4)  (2, 5)  (2, 6)

(3, 1)  (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

(4, 1)  (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4,6)

(5, 1)  (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

(6, 1)  (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)

There are total 36 outcomes.

There are 33 outcomes with sum greater than 3.

The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).

Hence, the probability that the sum of the dice is 9 is, 4/33.

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The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.

According to the question,

We have the following information:

3² × [tex]3^{x}[/tex] = 3²

We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.

Now, we have the following expression:

2+x = 2

x = 2-2

x = 0

Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.

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The total number of students at library using part part whole model is 13.

What is part part whole model ?

  The idea that numbers may be divided into parts, often known as the part-whole model or part-part-whole reasoning, is one that can be used to the study of mathematics. The relationship between the entire number and its component components will be clear to children utilising this model, which will aid learners in connecting addition and subtraction.

Here Number of student who leave library = 6

Number of students who stay at library = 7

Here we have to take  Number of student who leave library as one part and Number of students who stay at library as another part . Then

Total number of students at library at start = 6+7 = 13.

The part part whole model like,

=>        Total = 13

Part=6              Part=7

Hence the Total number of students is 13.

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