Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180degrees°.
In a​ triangle, the measures of the three angles are​ x, x+14​, and x−38. What is the measure of each​ angle

390 gallons of 90 % antifreeze must be mixed with 60 gallons of 15% antifreeze to get a mixture that is 80%

Solution:

Let "x" be the gallons of 90 % antifreeze

60 gallons of 15 % antifreeze

Then, (x + 60) is the gallons present in final mixture that is 80 %

Therefore, x gallons of 90 % antifreeze is mixed with 60 gallons of 15 % antifreeze to get a mixture that is (x + 60) gallons of 80 %

Thus, a equation is framed:

90 % of x + 15 % of 60 = 80 % of (x + 60)

Solve the above equation for "x"

[tex]90 \% \times x + 15 \% \times 60 = 80 \% \times (x+60)\\\\\frac{90}{100} \times x + \frac{15}{100} \times 60 = \frac{80}{100} \times (x+60)\\\\0.9x + 0.15 \times 60 = 0.8(x + 60)\\\\0.9x + 9 = 0.8x + 48\\\\0.9x - 0.8x = 48 - 9\\\\0.1x = 39\\\\ x = 390[/tex]

Thus 390 gallons of 90 % antifreeze must be mixed

Answer:

10 paperback and 5 hardcover books

Step-by-step explanation:

Please see attached picture for full solution.

Let's check:

total cost= 10(3) + 5(8)= $70 ✓

You could also try to solve the question by assuming John bought all paperback books first instead of all hardcover books. The answer should be the same.

Answer:

False

Step-by-step explanation:

Answer: 79.2 points

Step-by-step explanation: The word "average" is the same as the word "mean" so to find the average of the points scored in their first 5 games, we want to add up all the points and divide them by the number of games they played which is 5 games.

Let's begin by adding the numbers.

79 + 68 + 86 + 91 + 72

Adding these numbers, we get a sum of 396.

This will be divided by how many games they played which is 5.

396 ÷ 5 = 79.2

This means that the average number of points scored is 79.2 points which could round down to 79 points but don't round unless the problem asks.

Answer:

3/15/8=2/1.25

Step-by-step explanation:

Answer:

see attached work shown

Answer:

-4x + 29

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]7x+14=7(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\7x+14=(7)(x)+(7)(2)\\\\7x+14=7x+14\qquad\text{subtract}\ 7x\ \text{from both sides}\\\\7x-7x+14=7x-7x+14\\\\14=14\qquad\bold{TRUE}\\\\\bold{CONCLUSION}\\\text{The equation has infinitely many solutions}[/tex]

Answer:

Step-by-step explanation:

1st year- 7*3=21

2nd year- 21*3=63

Answer:Q

Step-by-step explanation: EF is a segment. k is not uppercase. and MN is a line. So only Q could work.

[tex]\text{You're solving the equations:}\\\\4r - 5 = 17\\ 12 - 2s = 2\\\\\text{Solve for r:}\\\\4r-5=17\\\\\text{add 5 to both sides}\\\\4r=22\\\\\text{Divide both sides by 4}\\\\\boxed{r=5.5}\\\\\text{Solve for s:}\\\\12 - 2s = 2\\\\\text{Subtract 12 from both sides}\\\\-2s=-10\\\\\text{Divide both sides by -2}\\\\[/tex]

[tex]\boxed{s=5}[/tex]

An equation is formed when two equal expressions. The product of r and s is 27.5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation 4r - 5 = 17 can be solved for r as shown below,

4r - 5 = 17

Add 5 on both the sides of the equation,

4r - 5 + 5 = 17 + 5

4r = 22

Divide both the sides of the equation by 4,

4r / 4 = 22 / 4

r = 11/2

r = 5.5

The given equation 12 - 2s = 2 can be solved for s as shown below,

12 - 2s = 2

Subtract 12 from both the sides of the equation,

12 - 2s - 12 = 2 - 12

-2s = -10

Divide both the sides of the equation by -2,

-2s/-2 = -10/-2

s = 5

Now, the product of r and s can be written as,

r × s

= 5.5 × 5

= 27.5

Hence, the product of r and s is 27.5.

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Commutative property of multiplication

My explanation is attached in the image provided.

Step-by-step explanation:

$4.25×1 1/4=$4.25/1×5/4=$21.25/4=$5.25

Answer:it would cost 5.25

Step-by-step explanation:

Answer: 3(4) + .5(8) = 16

Step-by-step explanation:Replace b with 2p in the 1st equation

3p + .50(2p) = 16

3p + 1P = 16

4p = 16

p = 16/4

p = 4 tubes of pain

then

b = 2(4)

b = 8 brushes

Kara bought 4 tubes of paint and 8 brushes, given the total cost of $16, the price per tube of paint is $3, and the price per brush is $.50.

The question is asking how many tubes of paint and brushes Kara bought if she spent a total of $16, each tube of paint costs $3, each brush costs $0.50, and the number of brushes is twice the number of tubes of paint. To solve this problem, we can denote the number of paint tubes as x and the number of brushes as 2x.

So we set up the equation considering the total amount spent: $3x + $0.50(2x) = $16. This simplifies to:

So, she bought 4 tubes of paint and 2 times that number of brushes, which is 8 brushes.

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Answer:

  B, E

Step-by-step explanation:

It can be helpful to factor the first two terms:

  f(x) = x^2(x -7) +36

This can make it easier to evaluate the function for different values of x.

The answer choices suggest you need to know whether f(5) and f(-14) match the values given here.

  f(5) = 5^2(5 -7) +36 = -50 +36 = -14 . . . . matches choice B (and E)

  f(-14) = (-14)^2(-14-7) +36 = -21(196) +36 . . . . does not match choice A (or D)

__

The one remaining answer choice we need to consider is C. If we look at f(0) for this equation, we find it is (-5)(-10) +14 = 64, which does not match f(0) = 36 for the function given in the problem statement.

The only true answer choices are B and E.

_____

The remainder theorem tells you that f(a) = the remainder from f(x)/(x -a).

Answer:

Step-by-step explanation:

total weight is 4 tons.

ratio of weight of truck to weight of coal is 7:5....added = 12

so 7/12 of the total weight is the truck's

and 5/12 of the total weight is the coal

7/12 of 4 tons = 7/12 * 4 = 28/12 = 2 1/3 tons <== weight of truck

5/12 of 4 tons = 5/12 * 4 = 20/12 = 1 2/3 tons <== weight of coal

Answer:

all work is pictured and shown

Answer: 20%

Step-by-step explanation:

Percentage increase = increase / original value x 100

Increase = $12.00 - $10.00 = $2

Therefore :

% increase = [tex]\frac{2}{10}[/tex] x 100

% increase = 20

Answer:

20%

Step-by-step explanation:

12.00 - 10.00 = 2.00

2 divided by 10 = 0.2

100  multiplied by 0.2 which gives you 20%

Answer:

Part 1) The graph in the attached figure N 1

Part 2) The graph in the attached figure N 2

Step-by-step explanation:

Part 1) we have

Line 1: y-intercept: 3 ordered pair: (3, 4)

we know that

To draw a line we need a minimum of two points

Remember that the y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

(0,3) and (3,4)

Plot the points on a coordinate plane and connect them to graph the line

see the attached figure N 1

Part 2) we have

Line 2: y=-2x+2

Find the intercepts of the line

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]y=-2(0)+2=2[/tex]

The y-intercept is the point (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

[tex]0=-2x+2\\2x=2\\x=1[/tex]

The x-intercept is the point (1,0)

Plot the intercepts and connect them to graph the line

see the attached figure N 2

Answer:

Part 1) The graph in the attached figure N 1

Part 2) The graph in the attached figure N 2

Step-by-step explanation:

Part 1) we have

Line 1: y-intercept: 3 ordered pair: (3, 4)

we know that

To draw a line we need a minimum of two points

Remember that the y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

(0,3) and (3,4)

Plot the points on a coordinate plane and connect them to graph the line

see the attached figure N 1

Part 2) we have

Line 2: y=-2x+2

Find the intercepts of the line

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

The y-intercept is the point (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

The x-intercept is the point (1,0)

Plot the intercepts and connect them to graph the line

see the attached figure N 2

Answer:

c o s t = x \displaystyle P: \text{cos}t=x P:cost=x.

Step-by-step explanation:

The cosine of t is equal to the x-coordinate of point P

Answer:

OPtion 3 points

Step-by-step explanation:

See the attached figure.

As shown, we can notice that the coordinates of all the points are (-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4).

The figure will be a function if for each value of x there exist a unique value of y.

In the figure, for each value of x we have two values of y. So it is not a function. We need to remove any of ordered pairs that have same input values.

From (-3,2) and (-3,3), we need to remove one point.

From (1,4) and (1,-4), we need to remove one point.

From (2,-2) and (2,-4), we need to remove one point.

It means total we need to remove 3 points from this graph so that it will be a function.

So, the correct option is 3 points.

Answer:

7 , Monday, Tuesday, Wednesday, Thursday, Friday, then you have you r weekend Saturday, Sunday, then you restart the week . :)

Step-by-step explanation:

Answer:

7 days in 1 week

Step-by-step explanation:

Count the days. (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday)

Answer:

The arc length of the semicircle is half the circumference of the full circle

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=11 \end{cases}\implies C=2\pi (11)\implies C=22\pi \\\\\\ \stackrel{~\hfill \textit{a semicircle has half of that}}{C=\cfrac{22\pi }{2}\implies C=11\pi \implies C\approx 34.56}[/tex]

Answer:

300/9 = 33.33 repeating

Step-by-step explanation:

9 can go into 300, 33 times with a remainder of 3.

4 grams sample will be left after 1 year

Step-by-step explanation:

The decay function for percentage decay is given by:

[tex]y =a (1-r)^x[/tex]

Here,

a is the initial value

r is the rate

x is the number of time periods

Given

Initial value = 100 grams

Rate = 6% = 0.06

Time = 1 year = 52 weeks

Putting the values in the formula

[tex]y = 100 (1-0.06)^{52}\\y = 100(0.94)^{52}\\y = 4.00\ grams[/tex]

Hence,

4 grams sample will be left after 1 year

Keywords: Decay, percentage

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Answer:

first multiply length×width×height,of the carton

8×8×4=256

then multiply length×width×height for boxes

2×1×1=2

divide 256 by 2

256÷2=128

Answer:

The perimeter of the polygon is 48 cm.

Step-by-step explanation:

Given: [tex]\angle B \cong \angle D[/tex]

To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA

Since, [tex]\angle B \cong \angle D[/tex] and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".

From this statement we shall conclude,

The length of [tex]AB=5+6=11[/tex]

The length of [tex]BC=6+7=13[/tex]

The length of [tex]CD=7+6=13[/tex]

The length of [tex]DA=6+5=11[/tex]

Thus, the perimeter of the polygon is

[tex]\begin{aligned}\text {Perimeter} &=A B+B C+C D+D A \\&=11+13+13+11 \\&=48 \mathrm{cm}\end{aligned}[/tex]

Hence, the perimeter of the polygon is 48 cm.

Answer:

Step-by-step explanation:

Let the length b y

Width = 2x - 3

Perimeter = 18x + 4

And

Perimeter = 2(l + w)

18x + 4 = 2(y + 2x - 3)

Dividing through by 2

9x + 2 = y + 2x - 3

Making y as subject

y = 9x - 2x + 2 + 3

y = 7x + 5

The missing side is 7x + 5

The correct expression to simplify is:

[tex]1+4.25n + 3/2p -3+(-2p)+5/4n[/tex]

Answer:

[tex]5.5n-1/2p-2[/tex]

Explanation:

1. Given expression:

[tex]1+4.25n + 3/2p -3+(-2p)+5/4n[/tex]

2. Group like terms:

[tex](1-3)+(4.25n+5/4n)+(3/2p-2p)[/tex]

3. Simplify:

[tex]-2+5.5n-1/2p=5.5n-1/2p-2[/tex]

The total number of possible outcomes when rolling a six-sided number cube twice is 36. This is calculated by multiplying the 6 possible outcomes from the first roll with the 6 possible outcomes from the second roll.

When you roll a six-sided number cube two times, you create a series of possible outcomes that can be categorised by understanding that each roll is independent of the other. On the first roll, you have 6 possible outcomes (1, 2, 3, 4, 5, or 6), and for the second roll, regardless of what the first number was, you again have 6 possible outcomes. To find the total number of outcomes possible when rolling a cube twice, you multiply the number of outcomes for each event. So, we calculate the total outcomes with 6 (for the first roll) times 6 (for the second roll), which equals 36 possible outcomes.

This means that rolling two dice can lead to one of thirty-six different combinations, where the first number of the pair corresponds to the result of the first roll and the second number to the result of the second. For instance, if you first roll a 4 and then a 3, one possible outcome is (4,3).

It is important to note that when calculating probabilities for specific sums of the two dice, such as the probability of rolling a seven, the outcomes are not all equally likely. If we consider the sum of the dice, rolling a two is less likely than rolling a seven because there's only one combination (1,1) for a sum of two, while there are six combinations (1,6; 2,5; 3,4; 4,3; 5,2; 6,1) for a sum of seven.

The correct answer is option B, as the solution of  the equation:

[tex]\frac{1}{3 m}+\frac{6 m-9}{3 m}=\frac{3 m-3}{4 m}[/tex]  is [tex]\frac{23}{15}[/tex]

Solving this type of equation containing the fractions involves the mathematical operations like finding a common denominator, combining the fractions, eliminating the fraction denominators, cancelling common terms, distributing, adding/subtracting to both sides, simplifying, and dividing both sides by the same factor.

The Steps of calculation are as follows:

Let's verify the answer:

We had the equation:

[tex]\[\frac{1}{3m} + \frac{6m - 9}{3m} = \frac{3m - 3}{4m}\][/tex]

And we simplified it to:

[tex]\[\frac{6m - 8}{3m} = \frac{3m - 3}{4m}\][/tex]

Next, we cross multiplied:

[tex]\[4m(6m - 8) = 3m(3m - 3)\][/tex]

[tex]\[24m^2 - 32m = 9m^2 - 9m\][/tex]

We then brought all terms to one side:

[tex]\[24m^2 - 9m^2 - 32m + 9m = 0\][/tex]

[tex]\[15m^2 - 23m = 0\][/tex]

Factoring out m:

[tex]\[m(15m - 23) = 0\][/tex]

So, either m = 0 or 15m - 23 = 0.

If 15m - 23 = 0, then [tex]\(m = \frac{23}{15}\)[/tex].

Therefore, the correct answer is: b. [tex]\frac{23}{15}$[/tex].