Tomàs is thinking of a number. Thirteen fewer than three times his number is 305. Of what number is Tomás thinking?

Answer:

See explanation

Step-by-step explanation:

William is thinking of a number n.

Then

two times his number = 2n

five less than two times his number = 2n - 5

The result is between negative three and fifteen, so

[tex]-3\le 2n-5\le 15[/tex]

Solve this compound inequality. First, add 5:

[tex]-3+5\le 2n-5+5\le 15+5\\ \\2\le 2n\le 20[/tex]

Divide it by 2:

[tex]1\le n\le 10[/tex]

William's number is between 1 and 10

The compound inequality representing the range of numbers that William might be thinking of is 1 ≤ n ≤ 10.

We have,

Let's assume the number William is thinking of is "n."

According to the first clue, "five less than two times his number is between negative three and fifteen."

We can represent this using a compound inequality as follows:

-3 ≤ 2n - 5 ≤ 15

Explanation:

"two times his number" is represented as "2n."

"five less than two times his number" is "2n - 5."

So, the compound inequality shows that "2n - 5" is between -3 and 15. This means that the possible values of "n" should satisfy both inequalities:

-3 ≤ 2n - 5 and 2n - 5 ≤ 15

Alternatively, you can simplify the compound inequality to:

-3 + 5 ≤ 2n ≤ 15 + 5

Which becomes:

2 ≤ 2n ≤ 20

Finally, divide the entire inequality by 2 to isolate "n":

1 ≤ n ≤ 10

Thus,

The compound inequality representing the range of numbers that William might be thinking of is 1 ≤ n ≤ 10.

This means William's number "n" could be any integer from 1 to 10, including both 1 and 10.

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Answer: True

Step-by-step explanation: Just took the test

Mark runs 27 feet in 6 seconds.

To find out how many feet Mark runs in 6 seconds, we need to determine how many yards he runs in 6 seconds first. We are given that Mark runs 6 yards every 4 seconds, so we can set up a proportion: 6 yards / 4 seconds = x yards / 6 seconds. Cross-multiplying and solving for x, we find that x = 9 yards. Now, since there are 3 feet in 1 yard, we can convert 9 yards to feet by multiplying by 3: 9 yards * 3 feet/yard = 27 feet. Therefore, Mark runs 27 feet in 6 seconds.

Answer:

Value of x is 34

Step-by-step explanation:

The figure is a quadrilateral;

Angles given are; 2x°, 88°,108° and (3x - 6)°

We already know that the interior angles of a quadrilateral add up to 360°

Therefore, to get the value of x;

2x° + 88° + 108° + (3x - 6)° = 360

5x° + 190° = 360°

5x° = 170°

 x = 34°

Thus, the value of x is 34

Answer:

A

Step-by-step explanation:

count the lines on the bottom and top

The dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.

A coordinate plane is a two-dimensional plane or region formed by the intersection of two number lines.

One number line is horizontal and called the x-axis, and the other number line is vertical and called the y-axis.

The point where they meet is called the origin. Points on a coordinate plane can be located by using numbers on the x-axis and the y-axis.

Given that a rectangle shown on the coordinate plane, we need to find the dimensions of the same,

So, if we see the figure we are going to have that, the base is of 5 units, (no matter if the base is -5 we will consider it as 5 units)

And the height is about 4 units.

Hence, the dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.

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Answer:

A= 37.5ml

B= 37.4kg

C= $272

D= £199.50

Step-by-step explanation:

You have to find 15% of all of them and then minus 15% from the amount you were given.

Answer:

They will finish in time for Jamal to catch the bus.

Step-by-step explanation:

Jamal agreed to bring four dozen i.e. 48 cupcakes in for sale.

He started icing cupcakes at 7:40 a.m. at a rate of 3 cupcakes per minute up to 7:50 a.m. that is the time when he needs to be out of his house to catch his bus.

So, with in this 10 minutes (7:40 a.m. to 7:50 a.m.) he would be able to make (10 × 3) = 30 cupcakes.

Now, at 7:44 his older sister started icing cupcakes too. she iced them at a rate of 4 cupcakes per minute.

So, in this 6 minutes (7:44 a.m. to 7:50 a.m.) she will be able to make (4 × 6) = 24 cupcakes.

Therefore, in total Jamal will be able to made (30 + 24) = 54 cupcakes.

Since, 54 > 48 so, they will finish in time for Jamal to catch the bus. (Answer)

Answer:

c（-4，-17）q（0，-11）

Step-by-step explanation:

draw picture

the first one because it has a slope of 4/1 where the second one has a slope of 0

Answer:

B) {-8,-1,0,6)

Step-by-step explanation:

range is always y

Answer:

5 x 7/10 is equal to 3.5, therefore it lies between the whole numbers of 3 and 4.

The product of 5 times 7/10 is exactly 3.5.

To calculate 5 times 7/10, we multiply 5 by the fraction 7/10. This can be done using simple multiplication of the numerator (5 * 7 = 35) followed by dividing the result by the denominator (35/10), which simplifies to 3.5. Thus, 5 times 7/10 is 3.5.

When we are asked where the product lies between, it actually means we are looking for a range. Since we already know 5 times 7/10 equals 3.5, it would be accurate to say that the product lies between numbers that are smaller and greater than 3.5. However, the question seems to be incomplete because it does not provide the specific range to work within, so based on the provided calculation, we can only state the exact answer which is 3.5.

Step-by-step explanation:

[tex]Area \: of \: triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 3.2 \times 9.6 \\ = 1.6 \times 9.6 \\ = 15.36 \: {cm}^{2} \\ [/tex]

14.5 hours will it take Jess to fill his pool.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Jess new pool holds 1,624 gallons of water he can fill the pool at a rate of 112 per hour.

So, the number of hours taken to fill the pool

= 1624 / 112

= 14.5 hour.

Thus, the time taken 14.5 hour.

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Answer:

Step-by-step explanation:

3) divide by 3

18,6,2.....

4) 6 is subtracted

48,42,36.....

5) multiplied by 3

81, 243,729.....

6) multiplied by 2

32, 64 , 128......

7) 6 is subtracted

70,64,58,........

8) 12 is added

60,72,84,.......

9) divide by 2

32, 16, 8 ......

10) 5 is added

28,33,38.....

11)  13 is added

63, 76, 89,.......

12) 8 is subtracted

51, 43, 35,..........

Answer:

x           y

0          -7

1            -9

2            -5

3            5

Step-by-step explanation:

The give function is [tex]y=3x^2-5x-7[/tex]

Assuming the domain is :{0,1,2,3} then we substitute these values into the function and solve for the range.

When x=0, [tex]y=3(0)^2-5(0)-7=-7[/tex]

When x=1, [tex]y=3(1)^2-5(1)-7=-9[/tex]

When x=2, [tex]y=3(2)^2-5(2)-7=-5[/tex]

When x=3, [tex]y=3(3)^2-5(3)-7=5[/tex]

The table then becomes:

x           y

0          -7

1            -9

2            -5

3            5

Answer:

hi

Step-by-step explanation: srry

Question:

Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right. Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly. If Brian and Damien have the same score, which statement is true?

A) Brian and Damien both answered 2 fewer questions correctly than Chris did.

B) Brian and Damien both answered 4 more questions correctly than Chris did.

C) Brian and Damien both answered 2 more questions correctly than Chris did.

D) Brian and Damien both answered 4 fewer questions correctly than Chris did.

Answer:

Option C

Brian and Damien both answered 2 more questions correctly than Chris did

Solution:

Let "x" be the number of correct answers of Brian

Let "y" be the number of correct answers of Chris

Let "z" be the number of correct answers of Damien

The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right

[tex]x = 14 + \frac{1}{4}y\\[/tex] ---------- eqn 1

Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly

[tex]z = \frac{5}{4}y - 2[/tex] ---------- eqn 2

Brian and Damien have the same score

x = z -------- eqn 3

Therefore,

[tex]14 + \frac{1}{4}y = \frac{5}{4}y - 2\\\\\frac{5}{4}y - \frac{1}{4}y = 14+2\\\\y = 16[/tex]

Substitute y = 16 in eqn 1

[tex]x = 14 + \frac{16}{4}\\\\x = 14 + 4\\\\x = 18[/tex]

Therefore, by eqn 3,

z = 18

Thus we get,

Number of correct answers of Brian = 18

Number of correct answers of chris = 16

Number of correct answers of Damien = 18

Therefore, correct statement is:

Brian and Damien both answered 2 more questions correctly than Chris did

Answer:

Brian and Damien both answered 2 more questions correctly than Chris did.-B

Step-by-step explanation:

Answer:

a) UNIT PRICE of  potatoes is $0.56

b) UNIT PRICE of  broccoli  is $3.1

c) UNIT PRICE of  broccoli  is $0.98

Step-by-step explanation:

UNIT PRICE is defined as the price of 1 unit.

[tex]\textrm{Unit Price} = \frac{\textrm{Total cost on n products}}{\textrm{n}}[/tex]

Now, here in the given question:

1.  Cost of  4.5 pounds of potatoes is  $2.52

So, the unit price of potatoes  [tex]= \frac{\textrm{2.52}}{\textrm{4.5}} = 0.56[/tex]

⇒ 1 pound of potatoes cost $0.56

Hence,UNIT PRICE of  potatoes is $0.56

2  Cost of  2.5 pounds of broccoli is $7.75.

So, the cost of 1 pound of broccoli  [tex]= \frac{\textrm{7.75}}{\textrm{2.5}} = 3.1[/tex]

⇒  1 pound of  broccoli cost $3.1

Hence,UNIT PRICE of  broccoli  is $3.1

3.  Cost of 2.5 pounds of pears is $2.45.

So, the cost of 1 pound of pears  [tex]= \frac{\textrm{2.45}}{\textrm{2.5}} = 0.98[/tex]

⇒ 1 pound of pears cost $0.98

Hence,UNIT PRICE of  broccoli  is $0.98

Answer:

Potatoes - $0.56/pound.

Broccoli - $3.1/pound.

Pears - $0.98/pound.

Step-by-step explanation:

A shopper paid $2.52 for 4.5 pounds of potatoes.

So, the unit price of potatoes is [tex]\frac{2.52}{4.5} = 0.56[/tex] dollars per pound.

A shopper paid $7.75 for 2.5 pounds of broccoli.

So, the unit price of broccoli is [tex]\frac{7.75}{2.5} = 3.1[/tex] dollars per pound.

A shopper paid $2.45 for 2.5 pounds of pears.

So, the unit price of pears is [tex]\frac{2.45}{2.5} = 0.98[/tex] dollars per pound. (Answer)

A system of equations is simply a collection of multiple equations that are either consistent, inconsistent, dependent or independent.

The system of equations is given as:

Next, we plot the graph of both equations (see attachment)

From the attached graph, the solution to the system of equation is (2/3,2/3)

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Answer: your welcome :)

Step-by-step explanation:

Answer:

Diameter of a circle is twice the value of the radius

And to calculate the value of the circumference which could also be said to be the perimetre...

The formlae is given by: 2(pie)r.

Where pie = 22/7

And r = radius of the circle

So everytging is multiplied together

Step-by-step explanation:

Answer:

none

Step-by-step explanation:

you cant multiply or divide to make them equivalent

Answer:

CD/RQ = AB/PN

8/6 = AB/10

6AB = 80

AB = 40/3, so x = AD = (1/2)(40/3) = 20/3

The correct answer is B.

The value of length AD in the similar triangles is determined as 20/3. (Option B).

The length of segment AD is calculated by applying proportion formula as follows;

CD/RQ = AB/PN

The given parameters include;

The value of length AB is calculated as;

8/6 = AB/10

6AB = 80

AB = 40/3

The value of length AD is calculated as;

x = AD

AD = 1/2AB

AD = (1/2)(40/3)

AD = 20/3

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x=41

Step-by-step explanation:

139+x=180

180-139=41

x=41

Two angles whose sum is 180° are called supplementary angles. The measure of the unknown angle is 41°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The two of the given angles form a linear pair. Thus, the measure of the two angles together will be equal to 180°.

1.) An equation to represent the measures of the angles.

x + 139° = 180°

2.) Solving the equation to find the measures of the unknown angle,

x + 139° = 180°

x = 180° - 139°

x = 41°

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Answer:

it is a repetitive decimal

Step-by-step explanation:

Answer:

it is a repetitive decimal

Step-by-step explanation:

Answer:

You put 8i^2 instead of 12i^2.  You multiply -6i by -2i which equal -12i^2

Step-by-step explanation:

-7 + 6i - 14i+ 12i^2

-7 - 8i - 12

-19 - 8i

Answer:

the answer is A) 35°.

Step-by-step explanation:    

Solution

To solve this problem, we need to use the information given about the angles and arcs. We know that arc VY = 132° and ∠YUV = 41°.

We can use the properties of a triangle to find the measure of arc XV. Since arc VY and arc XV are supplementary angles (their sum is 180°), we can write the equation:

arc VY + arc XV = 180°

We are given arc VY = 132°, so:

132° + arc XV = 180°

Now, we can solve for arc XV:

arc XV = 180° - 132° arc XV = 48°

However, since the given options do not include 48°, we can use the information about ∠YUV to find the closest answer. Since ∠YUV = 41° and arc VY = 132°, we can find the measure of arc VY by adding ∠YUV to it:

arc VY + ∠YUV = 132° + 41° arc VY = 173°

Now, we can use this new value of arc VY and the fact that arc VY and arc XV are supplementary to find the closest answer:

arc VY + arc XV = 180° 173° + arc XV = 180°

Now, we can solve for arc XV:

arc XV = 180° - 173° arc XV = 7°

Since 7° is not among the given options, we can consider the closest option, which is 35°.

So, the answer is A) 35°.

Answer:

It takes 1.68 hours to catch up to them.

Step-by-step explanation:

The speed of robber = 71 mph

The  speed of police =  78 mph

The police  start 10 minutes  later

by that time robber would have travelled

[tex]distance = \frac{speed}{time}[/tex]

10 minutes  =0.166667 hours

then the distance  =  11.8 mph

Let them meet at distance x from the bank.

time taken by police to reach x , time =[tex]\frac{ x}{78}[/tex]----------------------(1)

time taken by robber in the same time = [tex]\frac{x-11.8}{71}[/tex]---------------(2)

Equating (1) and (2)

[tex]\frac{x}{78} =\frac{ x-11.8}{71}[/tex]

[tex]71 x = 78(x - 11.8)[/tex]

71x =78x - 920.4

920.4 = 78x - 71x

920.4 = 7x

x = 131.48

The distance where they catch up with the robber from the bank is 131.48 miles

speed of police = 78 mph

distance =  131.48  miles

time they catch up = [tex]\frac{131.48}{78}[/tex]

= 1.68 hours

$698.94

Step-by-step explanation:

M = P [r (1 + r) ∧n / ( (1 + r) ∧n) - 1) ]

P = the principal loan amount = $150,000

Annual percentage rate = 3.8%

r = monthly interest rate = 0.038 / 12 = 0.003166

Term in years = 30

n = number of payments over the loan’s lifetime monthly = 30 * 12 = 360

M = the total monthly mortgage payment

Using the formula,

M = 150,000 [0.003166 (1 + 0.003166)∧360 / ((1 + 0.003166)∧360) - 1]

M = 150,000 [(0.003166 * 3.120394) / (3.120394 - 1)]

M = 150,000 [0.009880 / 2.120394‬]

M = 150,000 * 0.004660 = $699 (rounded up value)

As per mortgage calculator we get the exact value

M = $698.94

Answer:

do you need the value of x?

x=7+6y+2z

-2(7+6y+2z)+5y+2z=-1 -7y=13+2z

-14-12y-4z+5y+2z=-1

-14-7y-2z=-1

-7y-2z=-1+14

-7y-2z=13

Answer:

x= -1, y= -1 and z= -1

Step-by-step explanation:

x-6y-2z= 7 (Equation 1)

-2x+5y-2z= -1 (Equation 2)

-5x+6y+5z= -6 (Equation 3)

The above three are your system of equations and you need x3 answers!

Use equations (1) and (2) to eliminate z. Multiply equation (1) by −1 and then add to equation (2) to eliminate z. Resulting in:

−x+6y+2z= -7 (1)

−2x+5y−2z= -1 (2)

Adding them together results in your 4th equation:

-3x+11y= -8 (4)

Use equations (1) and (3) to eliminate z. Multiply equation (1) by −5 and equation (3) by −2 and then add to eliminate z. Resulting in:

−5x+30y+10z= -35 (1)

10x-12y-10z= 12 (3)

Add them to get:

5x+18y= -23 (5)

Use equations (4) and (5) to solve for x. Multiply equation (4) by 18 and equation (5) by −11 and then add to eliminate y.

−54x+198y= -144

-55x-198y= 253

-109x=109 (Divide -109 from both sides to isolate x)

x= -1 <---- ANSWER 1

Substitute x=−1 into equation (4) to find:

−3x+11y= -8

-3(-1)+11y= -8

3+11y= -8 (Subtract 3 from both sides)

11y=-11 (Divide 11 from both sides to isolate y)

y=-1 <---- ANSWER 2

Now we can substitute x=−1 and y=−1 into equation (1) to find:

x-6y-2z= 7

(-1)-6(-1)-2z=7

-2z+5=7 (Subtract 5 from both sides to isolate z)

z= -1 <---- ANSWER 3

Hope this explains it for you! Enjoy! <3