2. Alonzo built a rectangular sign that measured 2 3/4 feet in length by 1 1/2 feet in width. a. What is the area of the sign?

The original speed of the train was 32 miles per hour.

We have a train. The train travels a distance equal to 288 miles. It is given that if the speed of a train is increased by 4 miles per hour from its original speed, then it takes 1 hour less to cover the distance. We need to find out the original speed of the train.

Let the original speed of the train be denoted by the variable "s". We can write the following equations using the given data:

s = 288/t

(s + 4) = 288/(t - 1)

We will substitute the value of "s" from the first equation into the second equation.

(288/t) + 4 = 288/(t - 1)

(288)×(t - 1) + 4×t×(t - 1) = 288×t

288t - 288 + 4t² - 4t = 288t

4t² - 4t - 288 = 0

t² - t - 72 = 0

t² - 9t + 8t - 72 = 0

t(t - 9) + 8(t - 9) = 0

(t - 9)(t + 8) = 0

The value of time cannot be negative, so the value of "t" is 9. Now, we will substitute this value into the first equation.

s = 288/t

s = 288/9

s = 32

Hence, the original speed of the train is 32 miles per hour.

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SOLUTION:

Step 1:

In this question, we are given the following:

How many subsets does the set T = {salsa, sour cream, queso, guacamole, pico de gallo} have?

Step 2:

The details of the solution are as follows:

Recall that:

The empty set and the set itelf are also part of the subsets that must be included as part of the number of subsets.

If a set has “n” elements,

then the number of subset of the given set is

Hence, the total number of subsets will be:

CONCLUSION:

The final answer is:

Answer:

-5+0=-5

(-6)+1=-5

-7+2=-5

Step-by-step explanation:

Answer:

46

Explanation:

In each number to the right of the equality sign, the tenths place is always the rightmost number in addition and the one place is the result of the addition.

For example, in 1 +3 = 34

Therefore, for 2 + 4 we have

Hence,

which is our answer!

Answer:

slope is -3

y intercept is 2

Step-by-step explanation:

3x+y=2 [subtract 3x from both sides]

y=-3x+2

slope is -3

y intercept is 2

Answer: The highest common factor of 91, 112 and 49 is 7

hope this helps :)

Answer:

9/2

Step-by-step explanation:

Answer

the commisoin is 270

Answer:

Step-by-step explanation:

I got 22 my friend hope i helped.

Answer:

$18

Step-by-step explanation:

50% of 40 is 20, so 40-20=20

10% of 20 is 2, so 20-2=18

total price=$18

the temperature in the morning was 1 degree celsius

then rise of 3 degree

so now the total temperature is 1 + 3 = 4 degree

so the temperature of the afternoon is 4 degrees.

Answer:

y<-7x+2

Explanation:

The slope-intercept form of a line is: y=mx+b

• When slope, m = -7

• y-intercept, b = 2

We have:

Since the boundary line is dashed, the inequality sign has to be < or >.

However, since the area below the line is shaded, we can now conclude that the inequality sign is: <

The inequality that matches this description is:

You have the square QRST, furthermore, you have that sides QS and QU are given by the following algebraic expressions:

QS = 16t - 14

QU = 6t + 11

Due to QRST is a square, the length of all sides are equal.

You can notice by the symmetry of the figure that QS = 2QU

Equal the expressions for QS and 2QU and solvde for t:

16t - 14 = 2(6t + 11) apply distribution property

16t - 14 = 12t + 22 add 14 both sides

16t = 12t + 22 + 14 subtract 12t both sides

16t - 12t = 22 + 14 simplfy like terms

4t = 36 divide by 4 both sides

t = 36/4 simplify the fraction

t = 9

Hence, the value of t is t = 9

The value of ∠L is 2.909° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".

An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.

Here,

Side k = 130

Side l = 710

Side m = 833.99204

Angle ∠L = 2.909°

Angle ∠M = 16.091°

Angle ∠K = 161°

Angle L=cos⁻¹((m²+ k² - l²)/2mk)

=cos⁻¹((834²+130²-710²)/2*834*130)

= 2.909°

Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠L is 2.909°.

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The dimensions of the golf hole found using the indicated variable expressions are as follows;

a. The area of the golf hole is 4·x² + 12·x

b. The perimeter of the golf hole is 8·x + 8

c. The perimeter of the golf hole if the area of the hole is 216 square feet is 56 feet

The perimeter of a geometric figure is found by the length of the boundary of the figure.

a. The area of the gulf hole is found as follows;

The area is a composite figure, which consists of a rectangle of length 3·x and width (x + 4) and a square of length x

Which indicates that the area is A = 3·x × (x + 4) + x×x = 3·x² + 12·x + x²

The area of the hole, A = 3·x² + 12·x + x² = 4·x² + 12·x

The area of the hole is A = 4·x² + 12·x

b. The perimeter of the hole is found as follows;

P = (x + 4) + 3·x + (x + 4) + x + x + x = 8·x + 8

The perimeter of the hole = 8·x + 8

c. The area of the golf hole = 216 square feet, which indicates;

4·x² + 12·x = 216

4·x² + 12·x - 216 = 0

x² + 3·x - 54 = 0

(x + 9)·(x - 6) = 0

x = 6 or x = -9

The perimeter of the golf hole is therefore;

P = 8 × 6 + 8 = 56

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Answer:

B and C

Step-by-step explanation:

Answer:

1)To find the mean, median, mode and midrange for each gender.

From the given data,

Male: 191,222,168,154,178,155,190,170,178,202,169,184,149,160,181,158

For Men:

Mean is,

Mean is 175.5625

Arrange the given data in ascending order,

149,154,155,158,160,168,169,170,178,178,181,184,190,191,202,222

Median is,

Median is 174

The mode is one of the values of the measures of central tendency. This value gives us a rough idea about which of the items in a data set tend to occur most frequently.

Mode is 178.

Female: 136,160,101,126,119,165,102,135,137,140,115,126,140,121,124

For Women:

Mean is,

Mean is 129.8

Arrange the given data in ascending order,

101,102,115,119,121,124,126,126,135,136,137,140,140,160,165

Median is 126

Mode is 126,140

Answer: 10.8 seconds

Step-by-step explanation:

[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]

Answer:

Below

Step-by-step explanation:

Look for   .9300 on the z-score table

   = z-score = + 1.48

  1.48 standard deciations =   1.48 * 15 = 22.2

110 + 22.2 = 132.2

132.2   is 1.48 standard deviations above the mean and is .9308 (93.08%)

Answer:

121 pi

Step-by-step explanation:

pi d =22 pi

divide both side by pi to find diameter

d=22

divide by 2 too find radius

11 is the radius

plugg 11 to pi r ²

121 pi

The x-coordinates of the points of intersection of the given function graphs are;

1) x = 0 and x = 2

2) x = -1

3) x = 0

The point of intersection of a graph is defined as the point or coordinates where two lines or curves meet each other.

1) In the first graph, we are given the functions as;

f(x) = -³/₄x² + 3x + 1

g(x) = 2ˣ

Thus;

From the graph, f(x) = g(x) is at (2,4 and (0, 1)

2) In the first graph, we are given the functions as;

f(x) = x² + 4x + 2

g(x) = (¹/₂)ˣ + 1

Thus;

From the graph, f(x) = g(x) is at (-1. 3)

C) In the third graph, we are given the functions as;

f(x) = -⁷/₃x - 3

g(x) = 2ˣ - 4

Thus;

From the graph, f(x) = g(x) is at (0, -3)

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y in equation 1

-28=3 is false, therefore the system of equations has no solution

Given:

Triangle ABC is mapped onto triangle ADE.

Required:

The transformation that maps triangle ADE similar to triangle ABC.

Explanation:

A dilation process from A by a factor 3 maps triangle ABC onto triangle ADE.

In the dilation process, the transformed angle value remains constant.

Also,

Therefore above transformation makes triangle ABC similar to triangle ADE.

Answer:

Thus from the explanation given above, the above transformation makes triangle ABC similar to triangle ADE.

The Sine rule formula is,

Given:

Let us solve for solve for the measure of angle B

Therefore,

Hence, there are no possible solutions for this triangle (OPTION C).

The constant of proportionality is 20.

What is constant of proportionality?

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

Given,

the recipe uses 5 cups of strawberries per 1/4 cup of sugar.

And let constant of proportionality is k.

that is

5 α 1/4

5 = k1/4

k = 5(4)

k = 20

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Mean is 5.25, Median is 5 and mode is 3.

Given,

In the question:

There are numbers:

3, 4, 5, 7, 6, 8, 8, 5, 3, 6, 4, 5, 3, 3, 7, 7.

To find the mean, median and mode.

Let's Know :

How do you find the mean median and mode?

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Now, According to the above statement :

To find Mean:

[tex]\frac{3+4+ 5+ 7+ 6+ 8+ 8+ 5+ 3+ 6+ 4+ 5+ 3+ 3+ 7+ 7}{16}[/tex]

= 84/16 = 5.25

For Median

Arrange in ascending order

3, 3, 3, 3, 4,4, 5,5,5, 6,6, 7, 7, 7, 8,8.

There is an even no. of observations. i.e., 16 numbers.

then, there is no single middle value; the median is then usually defined to be the mean of the two middle values: so the median of

Middle two values is : (5 + 5)/2 = 10/2 = 5

Middle value is 5

For Mode:

The mode is the number that occurs most often in a data set.

Mode is 3 .

Hence, Mean is 5.25, Median is 5 and mode is 3.

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Answer:

x=1

Step-by-step explanation:

Both graphs intersect at 1

Answer:

x=1

Step-by-step explanation:

They sectioned at 1

Answer:

Undefined

Step-by-step explanation:

The x-coordinates of two points on the line are the same, so the line is vertical. Thus, the slope is undefined.

Answer: The answer would be

B. 1/2

C. 1/3

Step-by-step explanation:

The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

Answer:

18

Step-by-step explanation:

Equation 9 x 4 / 2 = 18

First do 9 x 4 which is 36

Next do 36 / 2 which is 18

Also the "/" is another way to say to divide

SOLUTION

In mathematics, a ratio indicates how many times one number contains another.

And when we write quantities in ratio form, we represent ratio with the symbol :

For example: The ratio of A to B is written mathematically as A:B

Another important thing we must note when writing ratios is to always express both quantities in their simplest form.

With the above explanation, we can proceed in answering the question.

The ratio of adults to children which is 400 to 150, can be written mathematically in ratio form as:

Final answer: The ratio of adults to children is: