Being 10 miles apart, two cars started moving towards each other. After one hour they met, and during that time the first car covered 2 miles more than the second car. What was the speed of the first car?

Answer:

m<S = 45°

Step-by-step explanation:

The sum of the measures of the angles of a triangle equals 180 deg.

m<R + m<S + m<T = 180

3x + 2x + 3x = 180

8x = 180

x = 22.5

m<S = 2x = 2(22.5) = 45

In an isosceles triangle, the sum of the angles must equal 180 degrees. Given the angles labeled as multiples of x, solving for x gives 22.5 degrees, and m∠S is found to be 45 degrees.

The student is asking to find the measure of angle S in an isosceles triangle with vertices labeled R, S, and T, where sides RS and ST are equal, and the angles at R and T are labeled as 3x degrees, and angle S as 2x degrees. Since the sum of angles in any triangle is always 180 degrees, we can set up an equation by adding the angles together: 3x (angle R) + 2x (angle S) + 3x (angle T) = 180. Simplifying the equation gives 8x = 180, and solving for x gives x = 180 / 8 = 22.5 degrees. Finally, to find m∠S, we substitute x back into the expression for angle S: m∠S = 2x = 2(22.5) = 45 degrees.

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Answer:

The statement is true about whether A and B are independent eventa is fourth option:

A and B are not independent events because P(A/B)=0.375 and P(A)=0.25

Step-by-step explanation:

Let A be the event that the person rides the bus to school, then:

P(A)=75/300

P(A)=0.25

Let B be the event that the person has 3 or more siblings, then:

P(B)=24/300

P(B)=0.25

P(A/B)=9/24

P(A/B)=0.375

Like P(A/B)=0.375 is different to P(A)=0.25 the events are not independent

Answer. Fourth option:

A and B are not independent events because P(A/B)=0.375 and P(A)=0.25

correct answer is D

Look at the picture.

We must use the Pythagorean theorem two times.

first time:

[tex]d^2=4^2+6^2\\\\d^2=16+36\\\\d^2=52\to d=\sqrt{52}[/tex]

second time:

[tex]AB^2=1^2+(\sqrt{52})^6\\\\AB^2=1+52\\\\AB^2=53\to AB=\sqrt{53}[/tex]

Answer: D).-20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

keeping in mind that the x-intercept is where the graph touches the x-axis, and when that happens, y = 0, thus

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y=-3x+3 \\\\\\ \stackrel{\textit{setting y = 0}}{0=-3x+3}\implies -3=-3x\implies \cfrac{-3}{-3}=x\implies 1=x~\hfill \stackrel{\textit{x-intercept}}{(1,0)} \\\\\\ ~\hspace{34em}[/tex]

Answer: x-intercept = 1

Step-by-step explanation: To solve this problem, we need to remember that the y-intercept is the point where the line crosses the y-axis. So if our line has a y-intercept of 3, it crosses the y-axis up 3 units. So we start this problem by plotting the point (0,3) on y-axis and we can label that point A.

From there, our slope of -3 can be thought of as -3/1 so we go down 3 units and to the right 1 unit and we plot point B. Notice that point B happens to lie on the x-axis at (1,0) and it's important to understand that the x-intercept is the point where the line crosses the x-axis.

Since our line crosses the x-axis at the point (1,0), it as an x-intercept of 1. If you're given a y-intercept and a slope like you are in this problem, you won't always be able to determine the x-intercept but things work out nicely here because point B happens to lie on the x-axis.

I provided an image with the graph and my work as well.

Answer:

the answer should be 2,401 were going to St. Ives

Step-by-step explanation:

7 times 7 times 7 times 7 is 2401

Answer:

The answer is B. 7^0 + 7^1 + 7^2 + 7^3

[tex]p\%=\dfrac{p}{100}\\\\16\%=\dfrac{16}{100}=\dfrac{16:4}{100:4}=\dfrac{4}{25}\\\\16\%=\dfrac{16}{100}=0.16\\--------------------------------\\\\(16+(-2))^2=(16-2)^2=14^2=196[/tex]

We have three pairs of rectangles:

16ft × 6ft = 96ft²

2ft × 6ft = 12ft²

2ft × 16ft = 32ft²

S.A. = 2 × (96 + 12 + 32) = 2 × 140 = 280ft².

The surface area of a right prism is given by summing the areas of all its faces.

The surface area of a right prism can be calculated by finding the sum of the areas of all its faces.

Let's say the right prism has a rectangular base with length l, width w, and height h.

The surface area of the right prism would then be given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the given values into the formula will give us the surface area of the right prism.

For example, if l = 6ft, w = 8ft, and h = 7ft, the surface area would be:

Surface Area = 2(6)(8) + 2(6)(7) + 2(8)(7) = 192 + 168 + 112 = 472ft²

Therefore, none of the given options match the correct surface area.

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Final answer:

Only the set of ordered pairs listed in option a. (1,2), (2,4), (3,5) represents a function because each element of the domain is mapped to a unique element of the range.

Explanation:

To determine which of the given terms is a function, we recall that a function is a relation where each element of the domain (the first member of an ordered pair) is mapped to a single, unique element of the range (the second member of the ordered pair).

Option a - (1,2), (2,4), (3,5) has no repeated domain elements, so it is a function.

Option b - (1,2), (2,3), (1,5) has the domain element '1' mapped to two different range elements (2 and 5), so it is not a function.

Option c - (1,2), (2,4), (2,6) has the domain element '2' mapped to two different range elements (4 and 6), so it is not a function.

Option d - (1,2), (3,5), (3,7) has the domain element '3' mapped to two different range elements (5 and 7), so it is not a function.

Therefore, the correct answer is: a. Function 1 only.

Answer:

# left to right

Linear: 1,3,5

Non-linear: 2,4

Step-by-step explanation:

Anything in the y=mx+b format is automatically a linear function, therefore,

Linear: 1,3,5

Non-linear: 2,4

Answer:

= 36000 caps

Step-by-step explanation:

First we need to figure out how many minutes between 8 am and 3:30 pm

There are 7 hours and 30 minutes.

1 hour = 60 minutes

Multiply each by 7

7 hours = 7*60 minutes = 420 minutes

So 7 hours 30 minutes = 420 + 30 = 450 minutes

Bottle caps = rate * minutes

                   = 80 caps/minute * 450 minutes

                    = 36000 caps

The machine can put tops on 36,000 bottles between 8:00 a.m. and 3:30 p.m.

To calculate how many tops can be put on bottles at a factory between 8:00 a.m. and 3:30 p.m. by a machine that works at a rate of 80 bottles per minute, we need to determine the total number of minutes the machine operates between those times and then multiply that number by the rate of the machine.

First, let's find the difference in time from 8:00 a.m. to 3:30 p.m.:

Therefore, the machine operates for a total of 7 hours and 30 minutes. Since 1 hour equals 60 minutes, we have:

7 hours * 60 minutes/hour = 420 minutes

420 minutes + 30 minutes = 450 minutes

Now we multiply the total minutes by the rate of the machine:

450 minutes * 80 bottles/minute = 36,000 bottles

So the machine can put tops on 36,000 bottles between 8:00 a.m. and 3:30 p.m.

Answer:

Option 2.

Step-by-step explanation:

You are bisecting angle BAC  with pencil and compass.

Answer:

The angle bisector of a given angle.

Step-by-step explanation:

From the construction, < BAC is the given angle. With any radius, draw arc BC. With any radius and points B and C as the centers consecutively, draw arcs to intersect at O. Join O to A. Line /AO/ is the angle bisector of the given angle <BAC.

The construction illustrated is the angle bisector of a given angle.

Answer:

The radius = 7 units

Step-by-step explanation:

The diameter of a circle is twice the radius

d = 2r

If d =14 units

14 = 2r

Divide each side by 2

14/2 = 2r/2

7 =r

The radius = 7 units

Answer:

7 units

Step-by-step explanation:

Radius is the same as saying diameter divided by 2. 14 divided by 2 = 7, so the radius is 7 units.

Answer:

5h + 2c = 31

5c + 3h = 30

Step-by-step explanation:

Let h = HD video price

Let c = classic video price

Fiona bought 5 HD videos and 2 classic videos for $31

5h + 2c = 31

Iliana bought 5 classic videos and 3 HD videos for $30

5c + 3h = 30

This is the system of equations

5h + 2c = 31

5c + 3h = 30

Answer:

Correct answer on test is D. 5 x + 2 y = 31. 3 x + 5 y = 30.

Step-by-step explanation:

[tex]5+8e > 76\qquad\text{subtract 5 from both sides}\\\\8e > 71\qquad\text{divide both sides by 8}\\\\\boxed{e=\dfrac{71}{8}}[/tex]

[tex]e\cdot7<28\qquad\text{divide both sides by 7}\\\\\boxed{e<4}[/tex]

Looking at the graph When X is at 2 meals, the total cost is at Y = 3

Dividing the total coat of the mean by the number of means: 3 / 2 = 1.50

This means Fiona pays $1.50 per meal, which is less than the $1.75 Frank pays.

The answer is: Fiona's meals are less expensive.

Answer:

$377,358.49

Step-by-step explanation:

Let, the actual sales = $X

Given total sales amount including 6% of sales tax = $400,000

Therefore, (X+6% of X)= $400,000

⇒(X+X·6÷100)= $400,000

⇒(X+0.06X)= $400,000

⇒ 1.06X= $400,000

∴ X= $400,000÷ 1.06 = $ 377,358.49

Hence, the actual sales = $ 377,358.49

Answer:

$377,358.49

Step-by-step explanation:

We are given the total sales amount of $400,000 which has an included 6% of sales tax.

Assuming the actual sales to be x, we will use the following formula:

x + x * sales tax = total amount

x + x * 6% = $400,000

x + x * 0.06 = $400,000

x * 1.06 = $400,000

x = $400,000 / 1.06

x = $377,358.49

Therefore, a total sales amount of $400,000 that included a 6% sales tax yields actual sales of $377,358.49.

Answer:

x = 22.5 and y = 9

Step-by-step explanation:

Since the lines are perpendicular then the angles formed are right, hence

4x = 90 ( divide both sides by 4 )

x = 22.5

and 10y = 90 ( divide both sides by 10 )

y = 9

Answer: The measure of JK is 60 and the correct option is d.

Explanation:

It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.

The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .

According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.

By midpoint theorem,

Therefore the measure of JK is 60 and the correct option is d

The measure of FH = 24 units, measure of JL = 74, measure of KJ = 60

and, measure of FJ = 30.

What is coordinate geometry?

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

As given in the question,

F, G, and H are the midpoints of the sides of ΔJKL.

F is the midpoint of KJ, G is the midpoint KL, H is the midpoint of JL

Measure of the required sides are as follow:

FH = (KL / 2)                         (by midpoint theorem)

    = (48/2)

    = 24

JL = 2 x FG             (by midpoint theorem)

  = 2 x 37

  = 74  

KJ = 2 x GH             (by midpoint theorem)

   = 2 x 30

   = 60

FJ = GH = 30            (by midpoint theorem)

Therefore, measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.

Learn more about midpoints here :

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Answer:

The distance between both positions are 4.5

Step-by-step explanation:

we are given

Two similar artifacts are found—one at position (1,4) and the other at (5,2)

First point is (1,4)

x1=1

y1=4

Second point is (5,2)

x2=5

y2=2

now, we can use distance formula

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

now, we can plug values

[tex]D=\sqrt{(5-1)^2+(4-2)^2}[/tex]

[tex]D=\sqrt{20}[/tex]

[tex]D=4.5[/tex]

Answer:

Step-by-step explanation:

Answer:

The distance between both positions are 4.5

Step-by-step explanation:

we are given

Two similar artifacts are found—one at position (1,4) and the other at (5,2)

First point is (1,4)

x1=1

y1=4

Second point is (5,2)

x2=5

y2=2

now, we can use distance formula

now, we can plug values

To round 0.1287 to the nearest thousandth, we look at the next place value which here is 7. Since 7 is more than 5, we round up the thousandth place. Hence, 0.1287 becomes 0.129.

To round the number 0.1287 to the nearest thousandth, you need to look at the ten-thousandth place (which is the fourth numeral after the decimal point). In this number, the ten-thousandth place is 7. If this digit is 5 or above, we need to round up. If it is less than 5, we stay with the number as is. Since 7 is bigger than 5, we round up. Therefore, 0.1287 rounded to the nearest thousandth is 0.129.

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Answer:

= 7.5x-8

Step-by-step explanation:

Total cost = cost per yard * yard of fabric - coupon

total cost = 7.5 x - 8

y = 7.5x-8

Answer:

[tex]y=7.50x+8[/tex]

Step-by-step explanation:

For the equation, the amount of money is [tex]y[/tex], and the number of yards is [tex]x[/tex].

So, the problem says that the persona already have $8, which is constant, it wont' variate, that is, this is the independent term.

Then, it says the the fabric costs $7.50 per yard, and [tex]x[/tex] refer to yards, so this term would be [tex]7.50x[/tex].

Therefore, the equation to model this problem would be:

[tex]y=7.50x+8[/tex]

Answer:

actually it is x=0

Step-by-step explanation:

Answer: $45.00

Step-by-step explanation:

75 x 0.60 = 45

Answer:

$30

Step-by-step explanation:

First, change the percentage into decimal:

60% = 60/100 = 0.6

Multiply 75 with 0.6:

75 * 0.6 = 45

Note that this number 45 (0.6 of 75) is the amount off from the original price (75). Subtract 45 from 75

75 - 45 = 30

$30 is your answer

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Answer:

t(1) = -3.5, Recursive equation is t(n) = t(n-1) + 4.5

Step-by-step explanation:

t(n)=4.5n-8

Let find the sequence

Plug in n=1,2,3,4.....

n=1      t(1)=4.5(1) -8= -3.5

n=2      t(2)=4.5(2) -8= 1

n=3      t(3)=4.5(3) -8= 5.5

n=4      t(4)=4.5(4) -8= 10

so sequence is -3.5, 1, 5.5, 10................

Now we find the common difference

1 - (-3.5) = 4.5

5.5-1 = 4.5

10 - 5.5 = 4.5

common difference d = 4.5

Formula for recursive function is

t(n) = t(n-1) + d

We got d= 4.5

t(n) = t(n-1) + 4.5 , also t(1) = -3.5

Final answer:

The student seems confused between a linear and a quadratic equation. The provided equation is linear (t(n) = 4.5n - 8), while the supporting information describes how to solve a quadratic equation using the quadratic formula with specified coefficients.

Explanation:

The question posed by the student pertains to a recursive equation, which is a formula that defines each term of a sequence using preceding terms. However, the recursive equation mentioned (t(n) = 4.5n - 8) seems to be a simple linear equation rather than a recursive one. The student may be asking for a recursive form, but has provided a linear formula instead.

The additional information provided references a quadratic equation where the coefficients a, b, and c are given as 4.90, ±14.3, and ±20.0, respectively. The general form of a quadratic equation is at² + bt + c = 0. The solutions to this quadratic equation can be found using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). To find the solutions to the given quadratic equation, the values of a, b, and c would be substituted into the quadratic formula and the resulting expression solved.

For clarity, it seems there might be some confusion in the question as it mixes linear and quadratic equations. It is important to correctly identify the type of equation and its coefficients to proceed with finding a solution.

Answer:

$15 each

Step-by-step explanation:

$45/3 children= $15 each

Answer:

4 muffins

Step-by-step explanation:

just divide 8 by 2 or see how many times 2 can go into 8.

Answer:

4 muffins per cup of flour

Step-by-step explanation:

To solve this, simplify the ratio as much as possible

8 muffins : 2 cups of flour

You are solving for: x muffins : 1 cup of flour

Simplify. Divide common factors from both the numerator and denominator. In this case, divide 2.

8/2 = 4

2/2 = 1

4 muffins : 1 cups of flour is your simplified version.

4 muffins per cup of flour is your answer

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Answer: 49

==============================================

Explanation:

HI is parallel to KL, so this means that the two triangles can be proven similar through the AA (angle angle) similarity theorem.

Consequently, that means we can set up the proportion below

JH/JK = HI/KL

noticed how the left slant sides JH and JK pair up together on one side; the horizontal sides HI and KL pair up on the other side. I have the larger triangle's side lengths as the numerator for each side

Plug in the given values. Solve for HI

JH/JK = HI/KL

35/15 = HI/21

7/3 = HI/21

21*7 = 3*HI

3*HI = 147

HI = 147/3

HI = 49

This means that 35/15 = HI/21 turns into 35/15 = 49/21

Note: to check the answer that the last equation mentioned is true, we can subtract the fraction 49/21 from both sides to end up with 35/15 - 49/21 = 0. If you type "35/15 - 49/21" into your calculator, you should get 0, which will help confirm we have the right answer.

Answer:

a) Option b

b) 7524

Step-by-step explanation:

a) The survey is to estimate the number of adults.  Hence only adults should be surveyed and not senior citizens or houseowners. Since all adults cannot be surveyed a sample strictly at random of adults can be surveyed.  Since option b satisfies this, we select b as answer.

b) Given that in the survey of 25 adults 11 voted in the last election.

Hence out of 17100 adults, no of adults who voted in the last election would be

[tex]\frac{11}{25} *17100 = 7524[/tex]

So out of 17100, 7524 adults would have voted in the last election.