What is 8 times the sum of x and 15 as an algebraic expression (written answer)

The system of equations of two unknowns is formulated and solved.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}[/tex]

                                                              [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}[/tex]

                                                                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}[/tex]

The fraction that satisfies the request is [tex]\bf{\dfrac{20}{28}}[/tex] , since in [tex]\bf{\dfrac{-20}{-28}}[/tex] the negative signs are canceled and the first fraction is obtained.

Answer:

40°, 60°, 80°

Step-by-step explanation:

sum the parts of the ratio , 2 + 3 + 4 = 9 parts

the sum of the 3 angles in a triangle = 180° , then

180° ÷ 9 = 20° ← value of 1 part of the ratio , then

2 parts = 2 × 20° - 40° = ∠ A

3 parts = 3 × 20° = 60° = ∠ B

4 parts = 4 × 20° = 80° = ∠ C

Answer:

8

Step-by-step explanation:

Given algebraic expression:

5(x - 1) - 2

To:

Evaluate this expression using x = 3

Solution:

Evaluate by plugging x = 3 to this expression:

Simplify using PEMDAS.

We can conclude:

By evaluating x = 3 to the given expression,the answer will be 8.

Answer:

±2√3

Step-by-step explanation:

Equation :

x² -4 = 8

x² -12 = 0

Using the quadratic formula then simplifying gives you :

±2√3

I know this lacks explanation but please brainliest

Answer:

x=2 or -6

Step-by-step explanation:

×^2+4×-4=8

8 will enter inside and become -8

x^2+4x-4-8=0

x^2+4x-12

(x^2+6x)(-2x-12)

x(x+6)-2(x+6)

(x-2)(x+6)

x=2 or x=-6

Answer:

C

Step-by-step explanation:

The last reasoning is the side angle side theorem. In the whole proof, there is no mention of an angle. So the answer has to involve prooving that the angle in between the two sides that have been proven similar is the same in both traingles. This is best accomplished by statement C.

The graph of the function y = x+2 is steeper than the graph y = 2x-1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given functions are:-

The graph of the functions is attached with the answer below. In the graph, we can see that the slope of the graph y = x+2 is steeper than the graph of y = 2x - 1.

The two graphs intersect at the point ( 3,5 ) so it is the solution of the two linear equations.

Hence the graph of the function y = x+2 is steeper than the graph y = 2x-1.

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The probability will include:

The probability of P(A and 1) will be:

= 1/4 × 1/6

= 1/24

The probability of P(C and 2) will be:

= 1/4 × 2/6

= 1/12

The probability of P(B and 3) will be:

= 2/4 × 1/6

= 1/12

The probability of P(A and 4) will be:

= 1/4 × 2/6

= 1/12

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The area of the composite shape in the diagram given is: 100 square inches.

Area of a composite figure = sum of the areas of the shapes that make up the figure.

Area of the composite shape = 2(area of triangle) = 2(1/2bh)

Area of the composite shape = 2(1/2×10×10)

Area of the composite shape = 100 square inches.

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For a given central angle,  the length of the arc it intersects depends on the radius of the circle and the central angle.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

Length of an Arc = 2π×R×(θ°/360°)

where

θ is the angle, that which arc creates at the center of the circle in degree.

The measurement of the length of an arc formed by a central angle that intersects the circle at two points is given as,

[tex]\rm {Length\ of\ the\ arc} = 2\pi \times \text{Radius of the circle}\times \dfrac{\text{(Measurement of central angle)}}{360^o}[/tex]

Now, the length of the arc EF will be,

Arc EF = 2π × (AB) × (θ/360°)

Where θ is the measurement of the central angle.

Hence, For a given central angle,  the length of the arc it intersects depends on the radius of the circle and the central angle.

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Answer: Plato/edmentum sample answer  

Step-by-step explanation:

For a given central angle, the length of the arc it intersects depends only on the radius of the associated circle.

Answer:

true

Step-by-step explanation:

The statement is true because every graph associated a unique x-value for each y - value

The amount each friend does pay is £9.75

We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.

From the given information:

Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]

The cost of each friend = £9.75

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Answer:

length = 6cm , breadth = 4cm

Step-by-step explanation:

Let's assume length = l

breadth = b

Given perimeter of a rectangle = 20 cm

2(l+b) = 20

l+b = 20/2

l+b = 10

l = 10 - b____(1)

Given area of rectangle = 24 cm²

l×b = 24____(2)

(1) in (2) => l × b = 24

(10-b) × b = 24

10b - b² = 24

10b = 24 + b²

0 = b² - 10b + 24

b² - 10b + 24 = 0

b² + 6b + 4b + 24 = 0

b(b+6) +4(b+6) = 0

(b+4)(b+6) = 0

b+4 = 0. &. b+6 = 0

b = -4. b = -6

breadth must be less than length and it should be positive

So b = 4 cm

b=4 in (1)

(1)=> l = 10 - b

l = 10 - 4

l = 6

Answer:

90 meters

Step-by-step explanation:

so, what we know is that there are  90 seconds in one minute and a half.

Sam can run 6 meters per second. which means after 90 seconds, he should have run 540 meters.

Tom can run 7 meters per second. This means after 90 seconds, he should have run 630 meters.

630-540 = 90

give brainliest please!

hope this helps :)

Answer:

7 hours and 12 minutes

Step-by-step explanation:

there are 24 hours in a day, so multiply 6/20 by 24 to find the number of hours:

6*24/20 = 36/5 = 7  1/5 hours

we now know maria sleeps for 7 whole hours

next, there are 60 minutes in an hour, so multiply 1/5 by 60 to get 12 minutes

Answer:

0.65%

Step-by-step explanation:

i took the test

Step-by-step explanation:

[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf To \: find:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]

We know that,

[tex]\underline{\boxed{\sf (Radius)^2= (Slant height)^2-(height)^2}}[/tex]

[tex] \sf (Radius)^2 = (16)^2-(12)^2[/tex]

[tex] \sf (Radius)^2 = 256-144=112[/tex]

[tex] \longmapsto \sf Radius = \sqrt{112}≈10.6\:cm[/tex]

The value of x from the given triangle formed by the pot hanging from a brace is; x = 50°

We are given from the diagram that;

∠NMP = 110° and ∠NPM = 30°

Sum of angles in a triangle is 180°.

Thus;

∠MNP = 180 - (110 + 30)

∠MNP = 40°

Thus;

x = 90 - 40

x = 50°

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Answer:

C)   y = -3x + 15

Step-by-step explanation:

Let's start with the hours required, 15.  For each day worked we can subtract 3 hours.  X days would mean 3x hours.  Subtract that from the goal of 15 hours:

15 - 3x

The time remaining, y, is given by the equation 15 - 3x.

Rearrange the equation to match the format in the options,

y = 15 - 3x

y = -3x + 15

Option C

Answer:

A. Upward

B. (-2, -1)

C. X= -3, -1 ||| Y= 3

D. X=-2

Step-by-step explanation:

When written in factored form, 4w² -11w-3 is equivalent to (4w+1)(w−3).

When an expression is written as a result of the multiplication of some terms, then that multiplication form is called the factored form of that expression.

Example:   6 = 3 x 2 is a factored way of writing 6.

Given expression as

4w² -11w-3

4w²- 12 w− 1w − 3

(4w+1)(w−3)

Thus, the factored form of 4w² -11w-3 is (4w+1)(w−3).

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The equation for the relationship between the thickness and number of weeks is y = 3.8 - 0.2x

Ice lost at 7 weeks = 7(0.2) = 1.4 meters

Total thickness of ice before loss = Ice remaining after 7 weeks + Ice lost at 7 weeks

= 2.4 + 1.4

= 3.8 meters

The equation:

y = Total thickness of ice before loss - (Ice lost per week × Number of weeks)

= 3.8 - (0.2 × x)

y = 3.8 - 0.2x

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Answer: 37.9 inch the length of lead stripping .

Step-by-step explanation:

Given ,

Sides of windows are [tex]6\frac{4}{5}[/tex]  and [tex]15\frac{14}{25}[/tex]

[tex]= (6\frac{4}{5} + 15 \frac{14}{25} ) * 2\\ \\=\frac{34}{5} + \frac{389}{25} * 2\\\\ \frac{170}{25} + \frac{389}{25}* 2 \\\\= \frac{559}{25} * 2\\\\= \frac{948}{25} \\\\= 37.9 inch[/tex]

So , the answer is 37.9 inch

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{4 +3} \implies \cfrac{ -4 }{ 7 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{4}{7}}(x-\stackrel{x_1}{(-3)})\implies y-3=-\cfrac{4}{7}(x+3)[/tex]

The surface area of the rectangular prism with the dimensions that are stated is: 384 in.²

Surface area = perimeter of base × height of prism + 2(base area)

= (s1 + s2 + s3)L + 2(1/2bh)

Given the following:

Surface area = (6 + 8 + 10)14 + 2(1/2 × 6 × 8)

Surface area = 384 in.²

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The weight of the last child is 36 lbs.

The average weight of the three children is 60 lbs. The total weight will be:

= 60 × 3

= 180 lbs.

When another child is added, the weight is 54lb. The total weight will be:

= 54 × 4

= 216 lbs

The weight of the last child will be:

= 216 - 180

= 36 lbs.

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The answer is 0.75 because I took the test and that's what the answer was :)