Write an equation in slope intercept form for a line passing through the pair of points. Graph the line. (4, -2) and (8, -9)

Answers

Answer 1

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b the y-intercept.

The slope is computed as follows:

[tex]m\text{ =}\frac{y_2-y_1}{x_2-x_1}[/tex]

where (x1,y1) and (x2, y2) are two known points. Replacing with (4, -2) and (8, -9):

[tex]m=\frac{-9-(-2)}{8-4}=-\frac{7}{4}[/tex]

Replacing with the point (4, -2) and m = -7/4 into the general equation, we get:

-2 = (-7/4)4 + b

-2 = -7 + b

-2 + 7 = b

5 = b

Then, the equation is:

y = -7/4x + 5

The graph is

Write An Equation In Slope Intercept Form For A Line Passing Through The Pair Of Points. Graph The Line.

Related Questions

Let f(x) = 4x + 7. Find f-1(15)

Answers

[tex]f(x)=4x+7[/tex]

1. replace f(x) with y

[tex]y=4x+7[/tex]

2. Replace every x with a y and replace every y with an x

[tex]x=4y+7[/tex]

3. Solve for y:

[tex]\begin{gathered} 4y=x-7 \\ y=\frac{x-7}{4} \end{gathered}[/tex]

4. Replace y with f−1(x):

[tex]f^{-1}(x)=\frac{x-7}{4}[/tex]

Evaluate the inverse for x = 15:

[tex]f^{-1}(15)=\frac{15-7}{4}=\frac{8}{4}=2[/tex]

18. What is the value of x in the right triangle? 9 х A) 7 B) 777 C) 785 D) V7

Answers

Given a right-angled triangle

Where

[tex]\begin{gathered} \text{Hyp}=\text{Hypotenuse}=9\text{ units} \\ \text{Adj}=\text{Adjacent}=2\text{ units} \\ \text{Opp}=\text{Opposite}=x\text{ units} \end{gathered}[/tex]

The value of x can be deduced by using the Pythagorean theorem

The formula of the Pythagorean theorem is

[tex]\text{Hyp}^2=\text{Opp}^2+\text{Adj}^2[/tex][tex]9^2=x^2+2^2[/tex]

Solve for x

[tex]\begin{gathered} 9^2=x^2+2^2 \\ 81=x^2+4 \\ \text{Collect like terms} \\ x^2=81-4 \\ x^2=77 \\ \text{Square of both sides} \\ \sqrt[]{x^2}=\sqrt[]{77}^{} \\ x=\sqrt[]{77}\text{ units} \end{gathered}[/tex]

Hence, the answer is option B

A right triangle has one angle that measures 72°. What is the measure of the other acute angle?

Answers

If it is a right triangle, then it has a 90º angle.

As we know, the sum of the 3 angles in a triangle is equal to 180º. If we knoe the triangle has one angle that is 90º and the other that is 72º. Then what is the measure of the other acute angle (x):

[tex]\begin{gathered} 180º=\text{ 90^^ba + 72^^ba + x} \\ 180º\text{ -90^^ba -72^^ba= x} \\ 18º=\text{ x} \end{gathered}[/tex]

The measure of the other acute angle is 18º.

Use Example 1 as a model to evaluate the limitlim n→∞ nf(ci)Δxii = 1over the region bounded by the graphs of the equations. (Round your answer to three decimal places.)f(x) = x, y = 0, x = 0, x = 21Hint: Let ci = 21i2n2.

Answers

Answer:

Explanation:

please help me solve. I have the answer 36 but I want to make sure I did this correct

Answers

The diagram shows a right angled triangle with two other smaller right angled triangles inscribed in it.

The bigger of the two inscribed triangles is to the left with sides 9 and h.

The smaller of the two inscribed triangles is to the right with sides 4 and h.

Observe carefully, that the left triangle has

Shorter side = h

Longer side = 9

Similarly, the triangle on the right has

Shorter side = 4

Longer side = h.

Therefore we can use the ratio,

[tex]\begin{gathered} \frac{\text{shorter side}}{longer\text{ side}}=\frac{shorter\text{ side}}{longer\text{ side}} \\ \frac{h}{9}=\frac{4}{h} \\ \text{Cross multiply and you now have;} \\ h^2=36 \\ h=\sqrt[]{36} \\ h=6 \end{gathered}[/tex]

The altitude h, equals 6

The correct answer is option D, that is 6 units

Angelica's book head roses contains 5 white roses. The rest of the Roses are pink. What fraction of the bouquet is pink roses?

Answers

Well, I know there are 12 roses.

5 are white.

All you have to do is subtract 12 and 5. Once you do that you will have your answer!

Answer: 7/12 for pink roses.

i need to know everything i can be taught about Quadratic Relationships?

Answers

The line of symmetry is where one side of the graph is the same as the other side of the graph

Looking at the graph, the line at x = -1 , the left side is the same as the right side

The line of symmetry is x = -1

ΔΔΔΔΔΔΔ Simplified = What is the ratio of A to * ? What is the ratio of * to (A ) ? = =

Answers

[tex]\begin{gathered} \text{The symbol }\Delta\text{ occurs 14 times, } \\ \text{While the symbol }\ast\text{ occurs 28 times.} \\ \text{Therefore the ratio of }\Delta\text{ to }\ast\text{ is given as;} \\ \text{Ratio}=14\colon28 \\ \text{Ratio}=1\colon2 \\ \text{The ratio of }\ast\text{ to (}\Delta+\ast) \\ \text{Ratio}=28\colon(14+28) \\ \text{Ratio}=28\colon42 \\ \text{Ratio}=2\colon3 \end{gathered}[/tex]

find the length of the radius if the circumference is 13.2 round to one decimal place. use 3.14 for π

Answers

Given

[tex]\begin{gathered} \text{Circumference of Circle = 13.2 unit} \\ \pi\text{ = 3.14} \end{gathered}[/tex]

Required :

[tex]\text{length of radius (r) = ?}[/tex]

The formula for the circumference of a circle:

[tex]\text{Circumference of circle = 2}\pi r[/tex]

When we substitute and simplify:

[tex]\begin{gathered} 13.2\text{ = 2 }\times\text{ }\pi\text{ }\times\text{ r} \\ \text{making r the subject of formula} \\ r\text{ = }\frac{13.2}{2\text{ }\times\text{ 3.14}} \\ r\text{ = 2.1019} \\ \approx\text{ 2.1 unit (1.d.p)} \end{gathered}[/tex]

The transformation shown here maps each point on the preimage up 5 and right 4A) translation B) reflection C) rotation

Answers

Recall that, in geometry, a translation simply means moving without rotating, resizing, or anything else.

To translate a shape every point of the shape must move in the same direction and with the same distance.

Since the given transformations only move the shape 5 units up and 4 units right, then it is a translation.

Answer: Option A.

How much fencing does Susie need.Option d: x = 10 and 80 ft of fencing.

Answers

The area of a rectangle is given by the product of its dimensions.

If the rectangle area is 200 ft² and the dimensions are 2x and x, we have:

[tex]\begin{gathered} 200=2x\cdot x \\ 2x^2=200 \\ x^2=100 \\ x=10 \end{gathered}[/tex]

The total fencing needed is (2x+2x+x+x) from the perimeter and (x+x) from the internal fencing, so:

[tex]\begin{gathered} (2x+2x+x+x)+(x+x) \\ =6x+2x \\ =8x \\ =8\cdot10 \\ =80\text{ ft} \end{gathered}[/tex]

Therefore the correct option is d.

The posted speed limit is 45 miles per hour. Choose all the metric measures that are faster than 45 miles per hour. Customary and Metric Unit Equivalents DATA Length Weight/Mass Capacity 1 m - 3.28 ft 1 Oz - 28.35 g 1 gal - 3.79 L 1 m - 39.37 in. 1 kg - 2.20 lb 1 gt - 0.95 L 1 in. - 2.54 cm 1 metric ton (1) - 1.102 T 1 mi - 1.61 km A 45 km per hour B. 64.1 km per hour C. 86.4 km per hour D. 91 km per hour E. 112.3 km per hour

Answers

Converting 45 miles/hour to km/h, we have:

[tex]45\frac{miles}{h}\cdot(\frac{1.61\frac{\operatorname{km}}{h}}{1\frac{\text{miles}}{h}})=72.45\text{ km/h}[/tex]

Metric measures that are faster than 45 miles/hour = C. 86.4 km per hour / D. 91 km per hour / E. 112.3 km per hour​

Statistics show that the fractional part of a battery, B, that is still good after 6 hours of use is given by B = 4-0.011 What fractional part of the battery is still operatingafter 300 hours of use?AnswerHow to enter your answer (opens in new window)Keypad

Answers

Answer

Explanation

Given:

[tex]B=4^{-0.01t}[/tex]

where:

t=300 hours

To determine the fractional part of the battery after 300 hours of use, we plug in t=300 into B=4^-0.01t. So,

[tex]\begin{gathered} B=4^{-0.01t} \\ B=4^{-0.01(300)} \\ Simplify \\ B=4^{-3} \\ B=\frac{1}{64} \end{gathered}[/tex]

Therefore, the answer is:

[tex]\frac{1}{64}[/tex]

Josaleen bought a jacket for 50%. she paid 12% sales tax. what was the total price?

Answers

Step 1

Write out the given parameters

Price of Jacket = $50

Sales tax rate = 12%

Step 2

Write out the necessary formulas to find the total price of the Jacket

[tex]\text{Sales tax = price of jacket}\times\text{ sales tax rate}[/tex][tex]\begin{gathered} \text{Sales tax = }50\text{ x }\frac{12}{100} \\ \text{sales tax =\$6} \end{gathered}[/tex]

Total price = price of jacket + sales tax

Total price = $50 + $6 = $ 56

Find the surface area of a rectangle solid with edges of length 2cm,5cm, and 7cm

Answers

The surface area for a rectangular prism is given to be:

[tex]A=2(lw+lh+wh)[/tex]

where l, w, and h are the lengths of the solid.

From the question, we have:

[tex]\begin{gathered} l=2\text{ cm} \\ w=5\text{ cm} \\ h=7\text{ cm} \end{gathered}[/tex]

Therefore, the volume is calculated to be:

[tex]\begin{gathered} A=2((2\times5)+(2\times7)+(5\times7)) \\ A=2(10+14+35) \\ A=2(59) \\ A=118\text{ cm}^2 \end{gathered}[/tex]

The surface area is 118 square centimeters.

State all integer values of x in the interval [-4,3] that satisfy the following inequality 5x-5> -20

Answers

Inequality:

[tex]5x-5>-20[/tex]

The integer values included in [-4, 3] are: -4, -3, -2, -1, 0, 1, 2, and 3.

To know which are included, we have to solve the inequality as follows:

[tex]5x-5+5>-20+5[/tex][tex]5x>-15[/tex][tex]x>-\frac{15}{5}[/tex][tex]x>-3[/tex]

Then, all the values greater than -3 are included, but not -3.

Answer: x = -2, -1, 0, 1, 2, and 3.

write and solve an addition equation to find x. perimeter=43mw= 15ml= 10m÷10m

Answers

Answer:

8 m

Explanation:

The perimeter of the figure is the sum of all the sides, so if the perimeter is 43 m, we can write the following equation:

15 m + 10 m + 10 m + x = 43 m

Then, add the similar terms:

(15 m + 10 m + 10 m) + x = 43 m

35 m + x = 43 m

Subtract 35m from both sides:

35 m + x - 35m = 43 m - 35 m

x = 8m

Therefore, the value of x is 8 m

Todd invests $4300 in two different accounts. The first account paid 9 %, the second account paid 7 % in interest. At the end of the first year he had earned $347 in interest. How much was in each account?

Answers

hello

the initial principal in each account is unknown. we have a combined principal here and also a combined interest.

interest A + interest B = total interest

the rate in account A = 9%

the rate in account B = 7%

let x represent the amount of money invested in A

[tex]\begin{gathered} 0.09\times x+0.07\times(4300-x)=347 \\ 0.09x+301-0.07x=347 \\ 0.02x+301=347 \\ \text{0}.02x=347-301 \\ 0.02x=46 \\ \frac{0.02x}{0.02}=\frac{46}{0.02} \\ x=2300 \end{gathered}[/tex]

the amount in the first account with an interest of 9% is $2300

now we can use this information to find the amount in the second account by simply subtracting $2300 from the sum total principal

the amount invested in both accounts which is $4300

[tex]\begin{gathered} y=4300-2300 \\ y=2000 \end{gathered}[/tex]

the amount invested in both accounts are $2300 and $2000 respectively

a math teacher instructed students to create a diagram and use it to classify the numbers listed below Which diagram correctly classifies the numbers

Answers

Theconstant number π has the following value:

π = 3.15149...

That is, is a number with infinite decimals and without any periodicity. This type of numbers are known as irrational numbers. Hence, number π is an irrational number.

Which conclusion does the diagram support?A. UV/VW=ZY/YXB. VY/WX=UZ/ VYC. UZ=1/2 WXD. VY=1/2 WX

Answers

∵ WX // VY // UZ

∵ WU and XZ are transversals

→ The transversals intersect the parallel lines into parts equal in ratio

[tex]\therefore\frac{UV}{ZY}=\frac{VW}{YX}[/tex]

We can switch VW with ZY to be

[tex]\frac{UV}{VW}=\frac{ZY}{YX}[/tex]

Then the answer is A

I need hoeing finding out the answer because I’m in confusion

Answers

ANSWER

C) d = 12h

EXPLANATION

Sophia earns $12 for every hour she babysits. If she babysits for h hours, then she will be paid h times the hourly payment: 12*h,

[tex]d=12h[/tex]

Please help this is due in an hour. the equation is q+q+.3q=180 pls help.

Answers

q=45

Explanation

Step 1

the sum of the internal angles of a triangle must be 180 , then

[tex]\begin{gathered} 3q+q+q=180 \\ \\ \\ \end{gathered}[/tex]

Step 2

add similar terms

[tex]\begin{gathered} 3q+q+q=180 \\ 4q=180 \end{gathered}[/tex]

Step 3

divide both sides by 4

[tex]\begin{gathered} 4q=180 \\ \frac{4q}{4}=\frac{180}{4} \\ q=45 \end{gathered}[/tex]

I hope this helps you.

200×200 divided by 20

Answers

[tex]\begin{gathered} \frac{200\times200}{20}=\frac{200}{20}^{}\times\frac{200}{1} \\ \frac{200}{20}=\frac{20}{2}=10 \\ \frac{200\times200}{20}=10\times200=2000 \end{gathered}[/tex]

The value of the numerical expression (200 × 200) / 20 will be 2,000.

Given that:

Expression, (200 × 200) / 20

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

Simplify the expression, then we have

⇒ (200 × 200) / 20

⇒ 200 × 10

⇒ 2,000

More about the value of the expression link is given below.

https://brainly.com/question/23671908

#SPJ6

desuon 28 OT 40 Let A x) = 7x- 4 What is (6)? O A. 38 ООО OB. 42 C. 48 O D. 46

Answers

f(x) is given by the expression

[tex]f(x)=7x-4[/tex]

Then, to evaluate f(6), substitute x for 6 in the expression above

[tex]\begin{gathered} f(6)=7(6)-4=42-4=38 \\ \Rightarrow f(6)=38 \end{gathered}[/tex]

The answer is 38, option A

What is the coordinate for the image of point H(-1,-5) under a 90 degree clockwise rotation about the origin?What is the mapping rule for finding the coordinates of a figure that isA) Rotated 180 degrees about the origin? -> (x,y)B) Rotated 90 degrees about the origins -> (x,y)

Answers

By definition, a Rotation is a transformation in which a figure is turned about a point called "Center of rotation".

In this case you know that the point H must be rotates 90 degrees clockwise about the Origin. Remember that the Origin is this point:

[tex](0,0)[/tex]

The rule for a 90 degree Clockwise rotation about the Origin, is:

[tex](x,y)\rightarrow(y,-x)[/tex]

Knowing that the Pre-Image is this point:

[tex]H\mleft(-1,-5\mright)[/tex]

You need to apply the rule in order to find the coordinates of it Image after the rotation indicated. This is:

[tex]H\mleft(-1,-5\mright)\rightarrow H^{\prime}(-5,1)[/tex]

The answer is:

[tex]H^{\prime}(-5,1)[/tex]

Lelani is making playdoh.The recipe she calls for 1 cup of flur,1 cup of water , 2 tsp of cream of tartar,1 /3 cup of salf, and 1 tbsp vegetable oil. Lelani accidentally put 1 /4 cup of vegetable oil in her mix instead of 1 tbsp.

There are 16 tbsp in 1 cup. How many tablespoons of oil did Leilani put in her mix?
1/64 is the answer
---------------------------------------------------------------------
A) What is the ratio of oil to flour in the original recipe
B)how much flour should Leilani add to her mix to match the recipe again
C)If Lelani wants to make her mixture match the recipe , what else should she add to her mixture?

Answers

Part a: Ratio of oil to flour; 1: 16.

Part b: Extra flour added is 3.

Part c: 3 cups of water, 1 cup salt and 6 tablespoon of cream of tartar are added.

What is defined as the ratio?The ratio is defined as a comparison between two quantities of the same unit to determine how much of each quantity seems to be present in the other. Ratios are divided into two types. The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groups.

For the given question;

The recipe is made using the ingredients-

1 cup of flur,1 cup of water , 2 tsp of cream of tartar,1 /3 cup of salf, and 1 tbsp vegetable oil.

Now, Lelani accidentally put 1 /4 cup of vegetable oil in her mix instead of 1 tbsp.

16 tbsp = 1 cup.

The tablespoons of oil did Leilani put in her mix -

16×(1/4) = 4  tablespoons of oil

Part a:  ratio of oil to flour

16 tbsp = 1 cup.

Oil: flour

1: 16

Part b: Extra flour added.

1/4 cup = 4 tablespoon

oil:tablespoon; 1:16

If added 3 cups of the flour,

x cu[s = 16 tablespoons

4 : (16 + 6x)

1: 16

16(x + 1) = 64

x = 3 (3 cups of extra flour is added)

Part c: Extra recipe added.

oil:water = 1 ; 16

oil: salt = 1:16/3

oil : cream of tartar = 1:2

1:16 = 4:x1  ; 1:16/3 = 4: x2   : 4:x3 = 1:2

Solving the equation.

Thus, 3 cups of water, 1 cup salt and 6 tablespoon of cream of tartar are added.

To know more about the ratio, here

https://brainly.com/question/2328454

#SPJ1

Answer:

A)  oil : flour = 1/16 cup : 1 cup

B)  3 cups of flour (4 cups in total)

C)  Water = 3 cups

     Cream of tartar = 6 tsp

     Salt = 1 cup

Step-by-step explanation:

Playdoh recipe:

Flour = 1 cupWater = 1 cupCream of tartar = 2 tspSalt = 1/3 cupVegetable oil = 1 tbsp

Part A

The ratio of oil to flour is:

1 tbsp : 1 cup

There are 16 tablespoons in 1 cup, so the ratio in cups is:

oil : flour = 1/16 cup : 1 cupPart B

Lelani accidentally put 1/4 cup of vegetable oil in her mix instead of 1 tbsp.  

Let x be the amount of flour needed:

[tex]\implies \sf \dfrac{1}{16} : 1 =\dfrac{1}{4}: x[/tex]

[tex]\implies \sf \dfrac{\frac{1}{16}}{1}= \dfrac{\frac{1}{4}}{x}[/tex]

[tex]\implies \sf \dfrac{1}{16}x=\dfrac{1}{4}[/tex]

[tex]\sf \implies x=\dfrac{16}{4}[/tex]

[tex]\implies \sf x=4[/tex]

Therefore, 4 cups of flour is needed for 1/4 cup of oil.

Assuming Lelani has already added the 1 cup of flour required by the recipe, she will need to add a further 3 cups of flour to match the recipe again.

Part C

As the recipe now calls for a total of 4 cups of flour rather than 1 cup of flour, simply multiply all the amounts of the other ingredients by 4:

Flour = 1 × 4 = 4 cupsWater = 1 × 4 = 4 cupsCream of tartar = 2 × 4 = 8 tspSalt = 1/3 × 4 = 4/3 cupsVegetable oil = 1 × 4 = 4 tbsp

Therefore, assuming she has already added the amount of each ingredient given by the recipe, she should add an extra:

3 cups of water6 tsp of cream of tartar1 cup of salt

Use the picture below to answer the question: For the statement "< D is supplementary to < A and < D is supplementary to < B, so < A is congruent to < B," there reason the

Answers

Answer:

The correct option is:

a. Congruent Supplements Theorem

Explanation:

If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.

This means < A and < D is supplementary to < B, so < A is congruent to < B.

This is the Congruent Supplements Theorem

the tigers scored twice as many points as the buzzers .the tigers scored. poilnts did the buzzers score?

Answers

The tigers and the buzzers

We know that

- the Tigers scored 8 points.

- this is twice as the score of the Buzzers.

Since

2 x 4 = 8

then, 8 is twice as 4.

Then the Buzzers scored 4.

Answer: 4

you roll a number cu

Answers

Question:

Solution:

A die has 6 faces with numbers 1 through 6. Three faces have even numbers, and 3 faces have odd numbers.

Each roll of the die can result in 6 different outcomes.

The total number of different outcomes of rolling a die 3 times are 6 * 6 * 6 = 216.

There are 3 possible even number outcomes on the first roll and another 3 possible even number outcomes on the second roll. The third roll needs to be a 3, so there is one single desired outcome of the third roll.

Total number of desired outcomes: 3 * 3 * 1 = 9

probability(even, even, 3) = 9/216 = 1/24

So the correct answer (there is an error in the typography) would be 124.

Am I wrong ? One tutor told me it was B and another said it was D

Answers

Answer:

B. 8x² + 4

Explanations:

A binomial expression consists of two terms joined together by an addtion or subtraction.

It should not include an equality or inequality sign since it is an expression and not an equation or inequality.

Observing the rules stated above, only option B is the correct choice

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