Explain how you can know whether a system of linear equations will have infinite solutions.

Answer:

t = -b 2a = -120/(-32) = 3.75 The height of the rocket is a maximum 3.75 seconds after its launch. To find the height we only need to plug into the model: s(3.75) = -16(3.752) + 120(3.75) + 80 = 305 The maximum height of the rocket is 305 feet.

Step-by-step explanation:

The maximum value of graph of function is (3.75,225).

We consider, the equation is y=a(x-0)(x-7.5)

Now, when x=6 and y = 144

144=6a(-1.5)

⇒a= - 144/9

⇒a= -16

Now,  y= -16(x-0)(x-7.5)

⇒ y= -16[tex]x^{2}[/tex]+120x

∴ x = -b/2a = -120/(-32) = 3.75

When x=3.75, then the value of y is maximum.

∴ [tex]y_{max}[/tex] = [tex]-16(3.75)^{2}+120*3.75[/tex]

          = 225

Hence, the maximum value of y is 225.

So, the required co-ordinate is (3.75,225).

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Answer:

a= 1/4 , h=8 , k = -12

Step-by-step explanation:

There is really not much to say.

[tex]y=\frac{1}{x}[/tex] , [tex]y=\frac{1}{4x-32}-12[/tex]

Factor the denominator by 1/4.

[tex]y=\frac{1}{4(x-8)}-12[/tex]

You got your formula: [tex]y=\frac{a}{x-h}+k[/tex]⇒[tex]y=a\frac{1}{x-h}+k[/tex]
a= 1/4 means to shrink due to it being fraction.

h=8 means 8 right

k = -12 means 12 down.

Answer:

a. x=4 or x=−10

b. x= 3/2 or x= −8

Step-by-step explanation:

(FOR LETTER A)

Step 1: Factor left side of equation.

(x−4)(x+10)=0

Step 2: Set factors equal to 0.

x−4=0 or x+10=0

x=4 or x=−10

(FOR LETTER B)

Step 1: Factor left side of equation.

(2x−3)(x+8)=0

Step 2: Set factors equal to 0.

2x−3=0 or x+8=0

x= 3/2

or x= −8

Answer:

508.9

Step-by-step explanation:

**Kind note:

Since there are two variables in one equation, it is impossible to determine a specific value for x and y. (Unless the trial-and-error method is used).

How to determine the value of x using the equation (16x - 8y = 72)?

To determine the value of "x", we need to isolate the x-variable on one side. The value (or expression) obtained on the opposite side of the x-variable will be the value of x.

How to determine the value of y using the equation (16x - 8y = 72)?

To determine the value of "y", we need to isolate the y-variable on one side. The value (or expression) obtained on the opposite side of the y-variable will be the value of y.

Determining the x-variable:

⇒ 16x - 8y = 72

⇒ 16x = 72 + 8y                            [Adding 8y to both sides of the equation]

⇒ 16x/16 = (72 + 8y)/16                [Dividing 16 to both sides of the equation]

⇒ x = 9/2 + y/2                               [Simplifying both sides of the equation]

⇒ x = (9 + y)/2                                     [Combining the denominators]

Determining the y-variable:

⇒ 16x - 8y = 72

⇒ 16x - 8y - 16x = 72 - 16x         [Subtracting 16x both sides of the equation]

⇒ -8y = 72 - 16x                              [Simplifying both sides of the equation]

⇒ -8y/-8 = (72 - 16x)/-8                [Dividing -8 to both sides of the equation]

⇒ -8y/-8 = 72/-8 - 16x/-8

⇒ -8y/-8 = -72/8 + 16x/8

⇒ y = -9 + 2x                                  [Simplifying both sides of the equation]

First simplify it to suitable form of slope intercept then you can get values

The pairs are

And so on

Answer:

s= -1

Step-by-step explanation:

I believe 7=-10s-3

(s=-1)

Answer: 29 7/8

Step-by-step explanation:

The height of wall will be 29.875 inch.

The height of the wall can be measured by the sum of total height of bricks and the height of mortar joint between the bricks.

According to question there is 4 mortar joint and 5 rows of bricks.

1 mortar joint is situated between 2 bricks. So, if the no. of bricks is n, then mortar joint between them will be n-1.

So, width of one mortar joint is= 3/4 inch

Width of 4 mortar joints = (3/4)*4=3 inch

width of one brick is= 5.375 inch

Width of 5 bricks = 5.375*5=26.875 inch

Height of the wall

= width of 4 mortar joints + width of 5 bricks

= 3+26.875

=29.875inch or 29 7/8 inch

Therefore, the height of wall will be 29.875 inch.

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The diameter of the spherical globe that has a surface area of about 1018 in.² is: 18 inches.

Surface area = 4πr², where r is the radius, which is half of the diameter.

The globe is a sphere with a surface area of 1018 in.².

1018 = 4πr²

Solve for r

1018 = 4πr²

1018/4π = r²

81.0 = r²

r = √81.0

r = 9 in.

Diameter = 2(r) = 2(9)

Diameter of the sphere = 18 in.

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Answer:

its $125

thank me later <3

The cost of labor, per hour, will be equal to $125.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Tristan needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.75 hours and charged him $50 for parts.

The cost for labor per hour is,

TC = 50 + 4.75x

643.75 = 50 + 4.75x

x = ( 643.75 - 50) / 4.75

x = $125

Therefore, the cost of labor, per hour, will be equal to $125.

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Answer:

2 1/2

Step-by-step explanation:

Turn both fractions into improper fractions, multiply the whole number by the denominator and add the numerator.

4 3/4

4 * 4 + 3 = 19

19/4

2 1/4

2 * 4 + 1 = 9

9/4

Now since she drank 2 1/4 gallons of juice, subtract 9/4 from 19/4.

19/4 - 9/4 = 10/4

Now turn back into a mixed fraction, do this by putting 4 into ten twice and taking the remainder and putting it as numerator:

4 * 2 = 8

10 - 8 = 2

2 1/2

Answer:

its 72 in cubed because you do the base area/2 x the height divided by 3 so the base area is 48 and divide by 2 is 24 and then multiply by the height of the pyramid which is 9 and that will give you 216 and divide by 3 which is 72

Step-by-step explanation:

please mark as brainliest

Answer:

Step-by-step explanation:

-x + 2y = 16

y = mx + 8

Start with the top equation. Add x to both sides.

-x + 2y + x = x + 16                     Combine the left

2y = x + 16                                  Divide by 2

2y/2 = (1/2)x + 1/2(16)

y = 1/2 x + 8

If m = 1/2, both equations together will give an infinite number of solutions.

Answer:

x^3(-x+3)(x+3)

Step-by-step explanation:

-x^5 + 9x^3

factor out x^3

x^3(-x^2+9)

9 and -x^2 are perfect squares so we can factor out a 3 and an x to get (-x+3)(x+3)

the fully factored form would be x^3(-x+3)(x+3)

Answer:

-x^3(x - 3)(x + 3).

Step-by-step explanation:

-x^5+9x^3

the greatest common factor = x^3 so we can write it as

x^3(-x^2 + 9)

= -x^3(x^2 - 9)

The expression in the parentheses is the difference of 2 squares so we have:

-x^3(x - 3)(x + 3)   Answer.

Answer:

shoe size (US) 6

Step-by-step explanation:

Mode = most frequently occurring data value

From inspection of the table, we can see that the highest frequency (most number of women) is 20, so therefore the modal class of the data is shoe size (US) 6.

Answer:

Step-by-step explanation:

Answer:

D.) (x + 8)

Step-by-step explanation:

Which two values multiply to (-24) and add to (5)?

These values are (-3) and (8):

-3 x 8 = -24

-3 + 8 = 5

As such, the factors include these two values. One of the factors (x + 8), is one of the answer choices.

x² + 5x - 24 = (x - 3)(x + 8)

Answer:

x>=324

Step-by-step explanation:

sqrt(x) > = 18      square both sides of the equation

x >= 324

Answer:

(a)  y = 34.27 + 7.79x

(b)  r = 0.98 (nearest hundredth)

(c)  strong, positive correlation - as the students spends more time studying, their test scores increase.

Step-by-step explanation:

Correlation measures how closely two variables are linked.

If two variables are correlated, you can draw a line of best fit on the scatter plot.

Linear regression is a method for finding the equation of a line of best fit on a scatter plot.

The regression line of y on x is:  y = a + bx

where a = y-intercept  and  b = gradient

If b is positive, the variables are positively correlated.

If b is negative, the variables are negatively correlated.

Inputting the data from the table into a calculator and using the statistical function:

a = 34.27272727

b = 7.792207792

Therefore, the linear equation is:

y = 34.27 + 7.79x

The correlation coefficient is the Product Moment Correlation Coefficient (r) and measures the strength of the linear correlation between two variables.

Again, inputting the data from the table into a calculator and using the statistical function:

r = 0.9815741571

⇒ r = 0.98 (nearest hundredth)

The r value is always between +1 and -1.  The closer it is to +1 or -1, the stronger the correlation between the two variables.

Therefore, as r is very close to +1, the correlation coefficient suggests a strong, positive correlation.  In the context of the problem, this suggests that as the students spends more time studying, their test scores increase.

Answer:

You would get 8 cupcakes

Step-by-step explanation:

Since we're splitting C (cupcakes) with P (people) and we know that c = 88 and p = 11 we have to do the equation c / p or 88 / 11 which equals 8.

Answer:

Less than 1 kg

Step-by-step explanation:

1 gram = 0.001kg

So 60g = 0.06kg

If a miniature model of the pyramid is 3 inches wide. The volume of the model is 4.5.

Pyramids square bases  are twice as wide as they are tall

Model of pyramid=3 inches wide

First step is to find the model height

Let Model height=x

2 × height=weight

2x=3

x=3/2

x=1.5

Second step is to calculate the volume of model:

Volume of model=3×3×1.5×1/3

Volume of model=4.5

Therefore the volume of the model is 4.5.

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Answer:

B.

Step-by-step explanation:

x² + 13 = 8x + 37

Answer:

37 decreased by 20% is 29.6.

Step-by-step explanation:

To do this, what we do is simply take 20% of 37 and subtract it from 37.

20% of 37. A trick to easily figure this out is multipling 37 by 20 and dividing by 100.

37*20 = 740

740 / 100 = 7.40

37 - 7.40 = 29.6

37 decreased by 20% is 29.6.

Answer:

(2, -7)

x = 2

y = -7

Step-by-step explanation:

Let's solve this system of equations by elimination.

Start by multiplying the first equation by 2:

[tex]2(4x)+2(3y)=2(-13)\\8x+6y=-26[/tex]

Next, multiply the second equation by 3:

[tex]3(-5x)+3(2y)=3(-24)\\-15x+6y=-72[/tex]

Notice that both equations now have a "6y", meaning we can subtract both equations and thereby eliminating the variable "y" from the equation:

[tex]8x+6y-(-15x+6y)=-26-(-72)\\8x+6y+15x-6y=-26+72\\23x=46[/tex]

Divide both sides by 23

[tex]x=2[/tex]

Substitute 2 for "x" to solve for "y".

[tex]4x+3y=-13\\4(2)+3y=-13\\8+3y=-13[/tex]

Subtract 8 from both sides:

[tex]3y=-21[/tex]

Divide both sides by 3:

[tex]y=-7[/tex]

Therefore the answer is:

[tex](x, y)=(2, -7)[/tex]

Additional Comments:

Note that we can only divide, subtract, multiply, or add both sides of the equation by the same quantity due to the Division, Subtraction, Multiplication, or Addition Property of Equality. These properties state that if you divide/subtract/multiply/add one side of the equation by one quantity, you must do the same to the other side of the equation so that it remains an equation.

Answer:

Let me get my notes real quick. Give me a few seconds. Ok, in order to dermine propability you first do:
1: Determine the event (Like picking out 2 red marbles from a bag.) with 1 outcome (In this case, getting the marbles.)

2: Find the total amount of outcomes, like 1 7 2 9 1 2 2 2, (Example: What is the propability of geeting a 2? 4/8/50%)

3: Divide the number of events (How many times you've done it.) by the number of possible outcomes.

That's all there is.

Answer:

A = 81 pi  ft^2

Step-by-step explanation:

We know the circumference of a circle is given by

C = 2 * pi *r

18 pi = 2 * pi *r

Divide each side by 2 pi

18 pi / ( 2pi) = 2 pi r / ( 2pi)

9 = r

We can find the area by

A = pi r^2

A = pi ( 9)^2

A = 81 pi  ft^2

Answer:

1/6.

Step-by-step explanation:

Prob(Tail) = 1/2

Prob(gets number > 4 ,  that is a 5 or a 6) = 2/6 = 1/3.

So required probability = 1/2 * 1/3

= 1/6.

The individual probabilities are multiplied as the 2 events are independent.

The probability that Mario gets tails and rolls a number greater than 4 is,

⇒ 1 / 6

The term probability refers to the likelihood of an event occurring. 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.

Given that;

Mario flips a coin, then rolls a standard six-sided number cube.

Now, We get;

The probability to get tails is,

⇒ 1 / 2

And, The probability to get a number greater than 4 (5 and 6) is,

⇒ 2 / 6

⇒ 1 / 3

Thus, The probability that Mario gets tails and rolls a number greater than 4 is,

⇒ 1/2 × 1/3

⇒ 1 / 6

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Apply Pythagorean theorem

Option D

Answer:

[tex]\sf D) \sqrt{77} \: ft [/tex]

Step-by-step explanation:

Given that,

→ Perpendicular (x) = ?

→ Hypotenuse (h) = 9 feet

→ Base (b) = 2 feet

Now by using the Phythagoras theorem,

→ (Hypotenuse)² = (Perpendicular)² + (Base)²

→ (h)² = (x)² + (b)²

→ (9)² = (x)² + (2)²

→ 81 = (x)² + 4

→ (x)² = 81 - 4

→ (x)² = 77

→ [ x = √(77) ]

Thus, length of remaining side is √(77) ft.

Answer:

See below

Step-by-step explanation:

The pie chart gives the percentage of the $ 4675 that goes to each expense

Housing     16 %        .16* 4675 = $ 748

Food           16%        .16 * 4675 = $748

Childcare    18%       .18 * 4675 =  $ 841.50

Trnsport       13%      .13 * 4675 = $ 607.75

etc      I think you can do the others---- right ?

Answer:

A. 5.4

Step-by-step explanation:

I think... I haven't done this sort of question in a while