Write the equation of the given circle.

center (1, -5)
radius of 10

Answer:

2x + 7 = 3x - 5

Step-by-step explanation:

Since triangle RTS is isosceles, RT is congruent to RS. So you can set up the equation 2x + 7 = 3x - 5 to find x. Then you can input the value of x into 2x +7 or 3x - 5 to find the measure of the congruent sides.

Answer:

m = 1

Step-by-step explanation:

distribute and simplify the left side of the equation

m + 8m - 12 = - 3

9m - 12 = - 3 ( add 12 to both sides )

9m = 9 ( divide both sides by 9 )

m = 1

To find the fraction of candies that are either grape or lemon flavored, we add the fractions representing each flavor: 2/5 for grape and 3/10 for lemon. After finding a common denominator, we get 4/10 + 3/10, yielding 7/10 of the candies being either grape or lemon-flavored.

To find the fraction of candies that are either grape-flavored or lemon-flavored, we need to add the fractions that represent each flavor. We are told that 2/5 of the candies are grape-flavored and 3/10 are lemon-flavored.

First, we need a common denominator to add these two fractions. The least common denominator for 5 and 10 is 10. We can convert 2/5 to a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. This gives us 4/10. Now we can add:

4/10 (grape flavored)

+ 3/10 (lemon flavored)

= 7/10 (either grape or lemon flavored)

Hence, the fraction of the candies that are either grape-flavored or lemon-flavored is 7/10.

Answer:

[tex]4(2y-9)[/tex]

Step-by-step explanation:

To begin factoring the expression [tex]8y-36[/tex], we use the GCF or greatest common factor. The greatest common factor is the greatest number that will divide into two or more values. We start to find it by factoring each term:

[tex]8y: 2*4*y[/tex]

[tex]-36: -1*4*9[/tex]

We notice the only common factors is 4.

We write in the form 4(____+_____). We find the inside of the parenthesis by dividing each term by 4.

[tex]\frac{8y}{4} =2y[/tex]

[tex]\frac{-36}{4} =-9[/tex]

4(2y-9)

Answer:-8.1111111

Step-by-step explanation:

Step-by-step explanation:

Given inequality is [tex]y<\frac{3}{4}x+2[/tex].

To graph that inequality, first we need to graph the line [tex]y=\frac{3}{4}x+2[/tex]. Then shade it for the inequality symbol <.

Graphing line can be done using two points.

plug x=0 into [tex]y=\frac{3}{4}x+2[/tex], we get:

[tex]y=\frac{3}{4}*0+2=2[/tex]

Hence first point is (0,2)

Similarly plug any random number for x say x=4, we get:

[tex]y=\frac{3}{4}*4+2=5[/tex]

Hence first point is (4,5).

Now we just need to graph both points and join them by a dotted line. because we have < not <=.

Next part is to test for shading.

Which can be done using any test point which is not on the given line. Say (0,0)

plug x=0,y=0 into [tex]y<\frac{3}{4}x+2[/tex].

[tex]0<\frac{3}{4}*0+2[/tex]

[tex]0<0+2[/tex]

0<2

which is true, hence shading will be in direction of test point (0,0).

Hence final answer will be the choice which looks like the graph attached below;

The correct answer is 2. A dashed line with the shaded area below the line.

To graph y < 3/4 x + 2, first find the y-intercept, which is the point where the line crosses the y-axis.

This happens when x is 0, so the y-intercept is 2.

The slope of the line is 3/4, so for every 3 units you move up, you must also move 4 units to the right.

Start at the y-intercept and move 3 units up.

Then, move 4 units to the right.

Repeat this process until you have graphed a few points.

The line should continue in this direction forever.

The shaded area below the line represents the values of y that are less than 3/4 x + 2.

Here are the possible answers:

The correct answer is 2. A dashed line with the shaded area below the line.

The dashed line indicates that the inequality is not strict, meaning that the line is allowed to touch the shaded area.

The shaded area below the line indicates that the values of y that are less than 3/4 x + 2 are represented by the points below the line.

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Answer:

B

Step-by-step explanation:

All circles are similar and therefore proportional. C/C' is the ratio of Circle C to Circle C'. Since it is 0.75, this means that C is 75% of C'. We know that radius of C will also be 75% of the radiuc of C'. We can the radius because we know the diameter of Circle C is 6. The radius is therefore 3. 3 is 75% of 4. So r/r' or 3/4=0.75. r/ must be 4.

Answer: B) 4

Step-by-step explanation:

Got this right on USA test prep

At the same rate, it would take Marisa 6/4 of an hour to paint the entire room. This is a ratio problem, specifically dealing with rates and proportional relationships.

Since Marisa painted 1/2 of her room in 3/4 of an hour, to paint the entire room would take double that time. When you double 3/4, you get 6/4. Therefore, at the same rate, Marisa would need 6/4 of an hour to paint the entire room.

This problem is a basic ratio problem related to rates and proportional relationships, common topics in middle school math. The rate in this case is painting speed, half a room per 3/4 of an hour. Thus, when we double the room space to be painted (from half a room to a full room) we should also double the required time.

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1) All three are right A.K.A 4

4) The answer is also 4).

Answer:

2.5 miles per hour

Step-by-step explanation:

ok, so we already know how long she walked in 1/2 hour and we need to find out how many miles in one full hour. So, i multiplied 1 1/4 times two to make up the one full hour and I got 2.5 miles. So the rate is 2.5 mph.

Speed of walking is 2.5 miles per hour

Given that;

Time taken to walk = 1/2 hour = 0.5 hour

Distance cover = 1¹/₄ = 5 / 4 = 1.25 miles

Find:

Speed of walking

Computation:

Speed of walking = Distance cover / Time taken

Speed of walking = 1.25 / 0.5

Speed of walking = 2.5 miles per hour

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Answer:

14/6

Step-by-step explanation:

To find the slope, we can put it into slope intercept form. So 6y=14x+5. So y=14/6+5/6.

Answer: n = -6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12= −1/3n +10

Step 2: Flip the equation.

−1/3n +10=12

Step 3: Subtract 10 from both sides.

−1/3n +10−10=12−10

−1/3n =2

Step 4: Multiply both sides by 3/(-1).

(3/−1) x (-1/3n) = (3/-1) x (2)

n=−6

Answer:

Step-by-step explanation:

On Monday: $2 on lunch.

On Tuesday: $1 on a snack.

On Wednesday: her siter gave her $3.

Now, before we graph the integers, first you need to think about those number and their meaning. If the number represents debt or expenses, then it must be a negative number. But, if the number represents money received, then it must be a positive number.

So, we have the following integer: -2, -1, 3.

If we graph these integers, it would be like the images attached shows.

Answer:

1. The angle ladder makes with the wall is 11.54°

2. The height above the ground at which the upper end of the ladder touches the wall is 9.80 m

Step-by-step explanation:

We see that the side opposite of ∠A and the hypotenuse (side opposite of 90 degree angle) of the triangle are known. The ratio that relates these two sides are SINE.

We know,

[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]

Thus we can write:

[tex]sin(A)=\frac{2}{10}\\sin(A)=\frac{1}{5}[/tex]

To find ∠A, we take the inverse sine of [tex]\frac{1}{5}[/tex]. Our answer is:

[tex]sin(A)=\frac{1}{5}\\A=sin^{-1}(\frac{1}{5})\\A=11.54[/tex]

Thus the angle ladder makes with the wall is 11.54°

Second part of the question asks for the height above the ground at which the upper end of the ladder touches the wall, this is the length of AC.

Given the angle we found, we see that the side AC is adjacent of the angle and we also know the hypotenuse. The ratio that relates these 2 sides is COSINE.

We know,

[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]

Thus, we can write:

[tex]cos(11.54)=\frac{AC}{10}[/tex]

Cross multiplying and solving for AC, gives us:

[tex]cos(11.54)=\frac{AC}{10}\\AC=10*cos(11.54)\\A=9.80[/tex]

Thus, the height above the ground at which the upper end of the ladder touches the wall is 9.80 m

Answer: 100/1220*792= 64.9 have cell phones.

Step-by-step explanation:

Answer:

The percentage of students with cell phone is 64.92%

Step-by-step explanation:

Given

Sample Size = 1,220

Number of student with cell phones = 792

Required

Percentage of students with cell phone

To calculate the percentage of students with cell phone, we take a ratio of the number of students with cell phone to the sample size.

Mathematically, this is represented as

[tex]Percentage = \frac{Students-with-cell-phone}{Sample Size}[/tex]

By Substitution,

[tex]Percentage = \frac{792}{1220}[/tex]

[tex]Percentage = 0.64918032786[/tex]

[tex]Percentage = 64.918032786[/tex]%

[tex]Percentage = 64.92[/tex]% Approximated to nearest hundredth

Hence, the percentage of students with cell phone is 64.92%

Answer:

B.

Step-by-step explanation:

The original function in 8 wide, the new function is 4 wide. That means the original function was shrunk by half (4/8)

(x,y)--> (1/2x, 1/2y) represents the dilation.

Dilation defines changing the size of an object without changing its shape.

This problem can be solved by following steps

= 1/2*8

= 4 units.

Y-axis of grey figure = 1/2*Y-axis of Black figure

= 1/2*8

= 4 units

Therefore,

(x,y)--> (1/2x,1/2y) represents the dilation.

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Answer:

Option B is correct

36 pizzas were topped with vegetables

Step-by-step explanation:

Let x be the number.

As per the statement:

At a pizzeria, the ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.

The ratio of pizza topped with meat to pizzas topped with vegetables = 4 : 3

then;

the number of pizza topped with meat = 4x

and

the number pizza topped with vegetables  = 3x

It is also given that the pizzeria made a total of 84 pizzas that day.

[tex]\text{Total Pizzas} = \text{Number of pizzas topped with meat}+ \text{Number of pizzas topped with vegetables}[/tex]

Substitute the given values we get;

[tex]84 = 4x+3x[/tex]

Combine like terms;

[tex]84= 7x[/tex]

Divide both sides by 7 we get;

12 = x

The pizza were topped with vegetables = 3x = 3(12) = 36

therefore, 36 pizzas were topped with vegetables

Answer:

The correct answer is option B.

Step-by-step explanation:

The ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.

Let the pizza's topped with meat be 4x

Let the pizza's topped with vegetable be 3x

Total pizzeria made a Saturday = 84

4x + 3x = 84

7x = 84

x = [tex]\frac{84}{7}=12[/tex]

Pizza's topped with meat = 4x = 4 × 12 = 48

Pizza's topped with vegetable = 3x = 3 × 12 = 36

12 pizzas were topped with vegetables.

Answer:

6

Step-by-step explanation:

the rate of change is given by the slope of the line

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

f(x) = 6x - 5 is in this form

with slope m = 6 ← rate of change

Answer:

6

Step-by-step explanation:

We are given the function f(x) = 6x-5 for which we have to determine its rate of change.

The rate of change is given by the slope of a line.

We know that the standard form of an equation of a line is given by:

y = mx + c

where m is the slope.

If we observe the given function, we can notice that is in the form y = mx + c where the slope (m) is 6.

Therefore, the rate of change for the function f(x) = 6x - 5 is 6.

Answer:

He needs to save $100 a month.

Step-by-step explanation:

Since Travis needs $300 in 3 months, you divide 300 by 3.

300/3 = 100

Therefore, Travis needs to save $100 a month.

Travis needs to save more than $100 each month for three months to afford an airplane ticket that costs more than $300.

To determine how much Travis needs to save each month to pay for his airplane ticket, which costs more than $300, we can set up an equation. Let's assume the minimum amount he needs for the ticket is $300. If Travis is saving for three months, he needs to divide the total cost of the ticket by the number of months he has to save.

Let the amount he needs to save each month be represented by a. Therefore, we have the following equation: 3a = 300, which simplifies to a = 300/3. Solving this, we find that a = $100.

However, since the ticket costs more than $300, he will need to save slightly more than $100 each month.

Answer:

20 lbs

Step-by-step explanation:

Answer:

Number of permutations = 5040

Step-by-step explanation:

We are given the word 'INNOVATIVE', that has total 10 letters.

Now, we are asked to form words using exactly 4 letters at a time i.e. out of 10 letters we are using 4.

Therefore, the number of permutations that can be formed using 4 letters are = P(10,4)

i.e. [tex]10_{P_{4} }[/tex]

= [tex]\frac{10!}{(10-4)!}[/tex]

= [tex]\frac{10!}{6!}[/tex]

= [tex]\frac{10*9*8*7*6!}{6!}[/tex]

= 10*9*8*7

= 5040

Answer: 5040

Step-by-step explanation:

npr = n! / (n - r)!

numbers of letters given = 10

permutation that can be formed using 4 letters at a time= 10 P ₄

=10! / (10 - 4)! = 10! / 6!

= 10 ×9 ×8×7 ×6! /6! ( the 6! will cancel out)

= 10×9 ×8×7=5040

Therefore, the number of permutations are 5040

Step-by-step explanation:

a. Given => m∠5 = 40°

b. Given => m∠2 = 140°

c. Same Side Interior Angle Theorem => The same side interior angles must add up to 180°, which in this case, it does. m∠4 and m∠2 are alternate interior angles, and so there measurements are the same. 180 - 140 = 40

d. Both angles are part of the "same-side interior angles", which means that there measurements should add up to 180°. Note that m∠5 = 40°, and m∠2 = 140° (Given). Set the equation

m∠5 + m∠2 = 180

Plug in the number for each angle

40 + 140 = 180

180 = 180 (True).

e. It is proven that the above measurements are congruent with their corresponding parts. This means that a || b through Converse of Same Side Interior angle Theorem.

~

Answer:

B 7

Step-by-step explanation:

Since the triangles are similar by AAA

We can use ratios to find the length x (which is PR)

5                 15

-------- = ------------

x               21

Using cross products

5 * 21 = 15 *x

Divide each side by 15

5/15 * 21 = 15x/15

1/3 * 21 =x

7 =x

Answer:

here is how i did it.

Answer:

The correct answer is option (C).

Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 > -48.1

Step-by-step explanation:

We have been given the freezing temperatures of cottonseed oil and coconut oil. The freezing temperature of cottonseed oil is -48.1 degree celsius and the same for coconut oil is 24.8 degree celsius.

We are supposed to compare the two freezing temperatures. We know that 24.8 is higher than -48.1, therefore, we can conclude that freezing temperature of coconut oil is higher than the freezing temperature of cottonseed oil because 24.8 is more than -48.1. Thus, correct answer is option (C).

Answer:

C

Step-by-step explanation:

Answer: ? = x + 1

Step-by-step explanation:

The perimeter of the garden is x + 3x + 1 + x + ?

The perimeter of the garden is also (6x + 2)

Therfore:

x + 3x + 1 + x + ? = 6x + 2

Collect like terms:

5x + 1 + ? = 6x + 2

Subtract 5x from both sides:

1 + ? = x + 2

Subtract 1 from both sides:

? = x + 1

You cannot find ? as a number, only in terms of x.

Answer:

280 calories

Step-by-step explanation:

200 / 50 = 4

1 gram = 4 calories

70 * 4 = 280

Therefore, there are 280 calories in 70 grams of cheese.