Write an equation: The sum of -7 and a is equal to 37

Answer:

b + 15

Step-by-step explanation:

Let:

"boys" = b

"girls" = g = 15

Note that: "sum" = addition.

Combine:

b + 15 is your numerical expression of your question.

~

Answer:

1 to 15

Step-by-step explanation:

1 boy/ 15 girls

Answer:

A. exactly $9.54

Step-by-step explanation:

First add up how much he bought

Sandwich    5.98

drink            2.99

apple            1.49

                    ---------

                     10.46

Then subtract this from 20

20.00

-10.46

--------------

 9. 54

When you get money back, you get exact change.

Answer:

i believe the answer is 9.5

Step-by-step explanation:

cos60 = c / 19 = 9.5

Answer:

B.

Step-by-step explanation:

To simplify something that looks like [tex]\frac{\text{whatever}}{\sqrt{a}-\sqrt{b}}[/tex] you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:

[tex]\sqrt{a}+\sqrt{b}[/tex].

If you had  [tex]\frac{\text{whatever}}{\sqrt{a}+\sqrt{b}}[/tex], then you would multiply top and bottom the conjugate of [tex]\sqrt{a}+\sqrt{b}[/tex] which is [tex]\sqrt{a}-\sqrt{b}[/tex].

The conjugate of a+b is a-b.

These have a term for it because when you multiply them something special happens.  The middle terms cancel so you only have to really multiply the first terms and the last terms.

Let's see:

(a+b)(a-b)

I'm going to use foil:

First:  a(a)=a^2

Outer: a(-b)=-ab

Inner:  b(a)=ab

Last:    b(-b)=-b^2

--------------------------Adding.

a^2-b^2

See -ab+ab canceled so all you had to do was the "first" and "last" of foil.

This would get rid of square roots if a and b had them because they are being squared.

Anyways the conjugate of [tex]\sqrt{17}-\sqrt{2}[/tex] is

[tex]\sqrt{17}+\sqrt{2}[/tex].

This is the thing we are multiplying and top and bottom.

For this case we have the following expression:

[tex]\frac {3} {\sqrt {17} - \sqrt {2}}[/tex]

We must rationalize the expression, so we multiply by:

[tex]\frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}}[/tex]

So, we have:

[tex]\frac {3} {\sqrt {17} - \sqrt {2}} * \frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {17- \sqrt {17} * \sqrt {2} + \sqrt {17} * \sqrt {2} -2} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {15}[/tex]

Thus, the correct option is option B.

Answer:

OPTION B

A perfect square trinomial can be factored using the pattern x²+2ab+b²=(x+a)² or x²-2ab+b²=(x-a)². The term 'a' is the square root of the last term, and 'b' is half of the second term's coefficient.

In mathematics, a perfect square trinomial is a type of second-order polynomial or quadratic function with a specific form. It is used in the factorization process, particularly when solving quadratic equations of the form ax² + bx + c.

A perfect square trinomial is a trinomial in the form x²+2ab+b² or x²-2ab+b². To factor such a trinomial, the pattern (x+a)² or (x-a)² is used where 'x' is the variable, 'a' is the square root of the third term, and 'b' is half of the coefficient of the second term. Hence, x²+2ab+b² factors to (x+a)², whereas x²-2ab+b² factors to (x-a)².

Take for example, the trinomial x²+6x+9. Here, 'a' is 3 (as √9=3) and 'b' is 3 (as half of 6 is 3). Both 'a' and 'b' are equal so we know the trinomial is perfect square and it factors to (x+3)².

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The factor a perfect square trinomial, use the pattern [tex](a+b)^2[/tex] = [tex]a^2[/tex]  +2ab+  [tex]b ^{2}[/tex] and simplify .

The pattern for a perfect square trinomial is a helpful algebraic expression that represents the square of a binomial.

It takes the form [tex](a+b)^2[/tex] = [tex]a^2[/tex] +2ab+[tex]b ^{2}[/tex]  

where a and b are variables. When faced with a trinomial that fits this pattern, you can use it to factor the trinomial efficiently.

To factor a perfect square trinomial, compare it with the pattern. If the trinomial can be expressed in the form [tex](a+b)^2[/tex] =[tex]a^2[/tex]+2ab+ [tex]b ^{2}[/tex] , then it is a perfect square trinomial.

Identify [tex]a^2[/tex]  ,2ab and [tex]b ^{2}[/tex] terms in the trinomial.

Once identified, you can write the factored form as [tex](a+b)^2[/tex].  This means the trinomial can be factored as  [tex](a+b)^2[/tex] where a is the square root of the first term, and b is the square root of the last term.

This process is essentially reverse-engineering the expansion of the perfect square trinomial pattern.

Factoring using the perfect square trinomial pattern can save time compared to other methods, making it a valuable tool in algebraic manipulations and simplifying expressions.

Answer:

= 52°

Step-by-step explanation:

The obtuse angle at O is twice the angle made at the circumference /by the same segment b.

=52×2=104°

The base angles that are made by isosceles triangle that has the apex with angle 104° equal to (180-104)/2=38°

The radii of a circle are equal and meet tangents at right angles.

Angle a= 90-38= 52°

Answer:

The probability that the proportion of Grammy award winners will be less than 47% is 0.6915

Step-by-step explanation:

* Lets explain how to solve the problem

- Suppose 46% of American singers are Grammy award winners.

- In a random sample of size 622 is selected

- We want to find the probability that the proportion of Grammy award

 winners will be less than 47%

* At first we must to calculate z

∵ [tex]z=\frac{P^{'}-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex], where

# P' is the sample proportion

# n is the sample size

# P is probability of success

∵ The sample proportion is 47% = 47/100 = 0.47

∴ P' = 0.47

∵ The sample size is 622

∴ n = 622

∵ The probability of success is 46% = 46/100 = 0.46

∴ P = 0.46

∴ [tex]z=\frac{0.47-0.46}{\sqrt{\frac{0.46(1-0.46)}{622}}}=0.5004[/tex]

- P(P' < 0.47) = P(z < 0.5004)

∵ P(z < 0.5004) = 0.6915

∴ P(P' < 0.47) = 0.6915

* The probability that the proportion of Grammy award winners will

 be less than 47% is 0.6915

Answer:

its D

Step-by-step explanation:

Answer:

D, The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

Answer:

4p(2-3q)

Step-by-step explanation:

Factor out 4 first:

8p-12pq​

4(2p-3pq) Next, factor out p like you would any other number.

4p(2-3q)

Answer:

4p (2-3q)

Step-by-step explanation:

Break each term into its prime factors

8p = 4*2p = 2*2*2p

12pq = 4*3pq = 2*2*3*p*q

The common factors are 2*2*p

That is the greatest common factor.  Take that outside the parentheses.  Leave what is left inside the parentheses

2*2*p( 2-3q)

4p (2-3q)

In a scenario where 'u' varies directly with 'v', the constant of variation, k is found by: k=u/v. Here, k becomes 6/-7. If we want to know the value for 'u' when v=4, we use the calculated k in our formula, resulting in u=4*(6/-7) which equals -24/7.

The question is about the direct variation between two quantities 'u' and 'v'. If 'u' varies directly with 'v', it means that multiplying or dividing one quantity will have the same effect on the other. We use the mathematical formula for direct variation to find the values: 'u' = kv, where k is the constant of variation.

So, we first find 'k' when u = 6 and v = -7. From our formula, k = u/v = 6/-7.

When we know the k, we can find u' when v = 4. Using the formula, 'u' = kv = 4 * (6/-7) = -24/7.

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Answer:

16

Step-by-step explanation:

8 / 2  * (2 + 2)

4 * (2 + 2)

4 * 4

16

Step-by-step explanation:

PEMDAS is ( Thank you google )

" PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete."

First, 2 + 2 = 4

Second, 8 divided by 2 is 4.

Third, 4x4= 16

Therefore, the answer is 16.

Answer:

3x² – 5x + 10

Step-by-step explanation:

(4x² – 2x + 8) - (x² + 3x - 2) =

Drop the first set of parentheses because it is unnecessary.

= 4x² – 2x + 8 - (x² + 3x - 2)

To get rid of the second set of parentheses, change every sign inside.

= 4x² – 2x + 8 - x² - 3x + 2

Now, combine like terms.

= 3x² – 5x + 10

Answer:

3x^2 -5x +10

Step-by-step explanation:

(4x² – 2x + 8) - (x² + 3x - 2)

Distribute the negative sign

(4x² – 2x + 8) - x² - 3x + 2

I like to line them up vertically

4x² – 2x + 8

-x² - 3x  + 2

---------------------

3x^2 -5x +10

Answer:

In the given   Δ ABC

the height will be CD

sin (A) = [tex]\dfrac{P}{H}[/tex]

sin (A) = [tex]\dfrac{CD}{b}[/tex]................(1)

now to find area of the ΔABC

area of the ΔABC  = [tex]\dfrac{1}{2}\times Base \times Height[/tex]

                                =[tex]\dfrac{1}{2}\times c \times CD[/tex]

from equation (1) we can substitute of the value of CD.

                               =[tex]\dfrac{1}{2}\times c \times b sin(A)[/tex]  

The base of ΔABC is c then the height is CD and the area of triangle is given by:   [tex]\rm \dfrac{1}{2}\times c \times b\times sin(A)[/tex]

Given :

AC = b

BC = a

c is the base of triangle ABC.

Solution :

In the given triangle ABC

[tex]\rm sin(A) = \dfrac{Perpendicular}{Hypotenuse}[/tex]

the height will be CD,

[tex]\rm sin (A) = \dfrac{CD}{b}[/tex]   ----- (1)

Area of the triangle ABC

[tex]\rm = \dfrac{1}{2}\times base\times height[/tex]

[tex]\rm =\dfrac{1}{2}\times c \times CD[/tex]   --- (2)

Now from equation (1) and (2) we get

[tex]\rm Area\;of\;\Delta ABC = \dfrac{1}{2}\times c \times b\times sin(A)[/tex]

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Answer with step-by-step explanation:

We are to write nine proper fractions (where the numerator is smaller than the denominator) and nine improper fractions (where the denominator is bigger than the numerator) using the number 3, 5 and 8.

Proper fractions:

[tex] \frac { 3 } { 5 },\frac { 3 } { 8 } \frac { 5 } { 8 }, \frac { 3 }{ 5 . 8 },\frac{5}{3.8}, \frac{8}{5.3},\frac{3}{5+8},\frac{5}{3+8}, \frac{5-3}{8} \imples\frac{3}{5},\frac{3}{8} \frac{5}{8},\frac{3}{40},\frac{5}{24}, \frac{8}{15},\frac{3}{13},\frac{5}{11}, \frac{1}{4}[/tex]

Improper fractions:

[tex]\frac{5}{3},\frac{8}{3} \frac{8}{5},\frac{40}{3},\frac{24}{5}, \frac{15}{8},\frac{13}{3},\frac{11}{5}, \frac{19}{3}[/tex]

Answer: Yes, you can write nine Proper Fractions and nine Improper Fractions  using the numbers 3,5,and 8.

Step-by-step explanation:

You need to remember that a fraction is Proper when the numerator is less than the denominator and it is Improper fraction when the numerator is greater than the denominator.

Knowing this, you can write the following nine Proper Fractions and nine Improper Fractions, using the numbers 3,5 and 8:

Proper Fractions:

[tex]\frac{3}{5},\frac{3}{8},\frac{3}{5+8},\frac{3}{8*5},\frac{5}{8},\frac{5}{3+8},\frac{5}{8*3},\frac{5-3}{8},\frac{8}{5*3}\\\\\\\frac{3}{5},\frac{3}{8},\frac{3}{13},\frac{3}{40},\frac{5}{8},\frac{5}{11},\frac{5}{24},\frac{1}{4},\frac{8}{15}[/tex]

Improper Fractions:

[tex]\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{8+3}{8},\frac{5+8}{3},\frac{3*5}{8},\frac{8*5}{3},\frac{3+8}{5},\frac{8*3}{5}\\\\\\\frac{5}{3},\frac{8}{5},\frac{8}{3},\frac{11}{8},\frac{13}{3},\frac{15}{8},\frac{40}{3},\frac{11}{5},\frac{24}{5}[/tex]

Answer:

Option D. 4:1

Step-by-step explanation:

we know that

If two solids are similar, then the ratio of the lengths of corresponding parts is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared

In this problem

The scale factor is equal to  [tex]\frac{2}{1}[/tex] (ratio of corresponding lengths)

therefore

The ratio of their surface areas is equal to

[tex](\frac{2}{1})^{2}=\frac{4}{1}[/tex]

Answer:

15 scarfs.

Step-by-step explanation:

The cost of 10 scarfs in Store A = 12 * 10 = $120.

The number of scarfs  that can be bought in Store A for $120

= 120 / 8 = 15.

15 scarfs

The cost of 10 scarfs in Store

A = 12 * 10 = $120

The number of scarfs  that can be bought in Store A for $120

= 120 / 8 = 15.

How to determine a price for your product?

To do so, you’ve got to be clear on:

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Answer:

y = -3x+4

Step-by-step explanation:

Slope intercept form of a line is given by  y = mx + b

Where

m is the slope

b is the y intercept.

To find m, we need to take any arbitrary 2 points and see how many units up/down and how many units right/left we need to go from one to another. Basically change in y by change in x.

Let's take 2 arbitrary points: (0,4)  &  (2,-2)

So we need to go -6 units from y = 4 to y = -2. We need to go 2 units from x = 0 to x = 2.

Hence slope is change in y by change in x, which is -6/2 = -3

b is the y-interceept, the place where it cuts the y axis. Looking at the graph, it is at y = 4

Now we can write the equation as :

y = -3x+4

Answer:

x = 1

Step-by-step explanation:

The axis of symmetry for a vertically opening parabola is a vertical line with equation

x = h

where h is the value of the x- coordinate the line passes through.

The axis of symmetry passes through the vertex 1, 4 ) with x- coordinate 1

Hence equation of axis of symmetry is x = 1

Answer:

The picture provided is the correct answer

Step-by-step explanation:

It needs to be greater than 4 or less than -4 in order for the absolute value to be greater than 7, so you're good.

Answer:

Step-by-step explanation: Sorry no time gtg : / (if you really need it I'LL ANSWER TOMMOROW

Answer:  The required simplified expression is -6xy.

Step-by-step explanation: We are given to simplify the following rational expression :

[tex]E=-\dfrac{18x^2y}{3x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property of exponents :

[tex]\dfrac{z^a}{z^b}=z^{a-b}.[/tex]

From expression (i), we get

[tex]E\\\\\\=-\dfrac{18x^2y}{3x}\\\\\\=-\dfrac{18}{3}x^{2-1}y\\\\=-6xy.[/tex]

Thus, the required simplified expression is -6xy.

Answer:

C. Reflection across the x-axis followed by the reflection across the y-axis.

Answer:

C

Step-by-step explanation:

Answer:

4.44 hours

Step-by-step explanation:

One pump can fill a swimming pool in 8 hours.

In 1 hour pump can fill the pool = [tex]\frac{1}{8}[/tex]

another pump can fill the swimming pool in 10 hours.

in 1 hour another pump can fill the pool = [tex]\frac{1}{10}[/tex]

Let the total time will it take together to fill the pool = x

[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{10}[/tex] = [tex]\frac{1}{x}[/tex]

[tex]\frac{5+4}{40}[/tex] = [tex]\frac{1}{x}[/tex]

[tex]\frac{9}{40}[/tex] = [tex]\frac{1}{x}[/tex]

9x = 40

x = [tex]\frac{40}{9}[/tex]

x = 4.44 hours

It will take 4.44 hours to fill the pool if both pumps are open.

Answer:

16

Step-by-step explanation:

You can choose

In total there are

[tex]2\cdot 2\cdot 4=16[/tex]

different outfits.

Another way to solve this problem is simply count all outfits:

Shirts [tex]Sh_1, \ Sh_2[/tex]

Pants [tex]P_1,\ P_2[/tex]

Shoes [tex]S_1, \ S_2,\ S_3,\ S_4[/tex]

All outfits

[tex]Sh_1P_1S_1, \\ Sh_1P_1S_2, \\ Sh_1P_1S_3, \\ Sh_1P_1S_4, \\ Sh_1P_2S_1, \\ Sh_1P_2S_2, \\ Sh_1P_2S_3, \\ Sh_1P_2S_4, \\ Sh_2P_1S_1, \\ Sh_2P_1S_2, \\ Sh_2P_1S_3, \\ Sh_2P_1S_4, \\ Sh_2P_2S_1, \\ Sh_2P_2S_2, \\ Sh_2P_2S_3, \\ Sh_2P_2S_4[/tex]

Answer:

A line that does not have an end to it.

Step-by-step explanation:

For example a line is forever, but if you put dots on the end, it will not be forever.

Answer:

A line segment is like a straight line, but has two dots on the edge of each end. A line segment has a starting and stopping point, which can help people tell the difference between other lines.

A line segment usually looks like this:

    \/   \/

 •----------•

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-9-0)^2+(1-10)^2}\implies d=\sqrt{(-9)^2+(-9)^2} \\\\\\ d=\sqrt{81+81}\implies d=\sqrt{162}\implies d\approx 12.73[/tex]

Answer:

Option B. [tex]YV=5\ units[/tex]

Step-by-step explanation:

we know that

The Intersecting Secant-Tangent Theorem, states that If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

In this problem

[tex]WZ^{2}=WV*WY[/tex]

substitute and solve for WV

[tex]6^{2}=WV*4[/tex]

[tex]WV=36/4=9\ units[/tex]

we have that

[tex]WV=WY+YV[/tex]

substitute

[tex]9=4+YV[/tex]

[tex]YV=9-4=5\ units[/tex]

Answer:

No correct answer.

Step-by-step explanation:

C: 2 or 3 is  1/2 the probability. The expectation is that you should get about 250 readings that are either 2 or 3.

A is not correct. It will land on an even number about 250 times. What should happen in theory is far different than what will happen when you try it. Exactly is too confining a word.

B: It will land on 1 about 1 out of every 4 times. 1/4 * 500 = 125. So B is not right.

D: Same as B. There is no answer.  

Answer:

see explanation

Step-by-step explanation:

Calculate the slope m of the line using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, 3) and (x₂, y₂ ) = (1, - 97)

m = [tex]\frac{-97-3}{1+7}[/tex] = [tex]\frac{-100}{8}[/tex] = - [tex]\frac{25}{2}[/tex]

Answer:

(7, - 3 )

Step-by-step explanation:

Solve the 2 equations simultaneously to find intersection.

Given the equations of the sides

2x + 3y = 5 → (1)

3x + y = 18 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the y- term

- 9x - 3y = - 54 → (3)

Add (1) and (3) term by term

(2x - 9x) + (3y - 3y) = (5 - 54) and simplifying gives

- 7x = - 49 ( divide both sides by - 7 )

x = 7

Substitute x = 7 into (1) or (2) for corresponding value of y

Substituting in (2)

21 + y = 18 ( subtract 21 from both sides )

y = - 3

Point of intersection = (7, - 3 )

Final Answer:

The coordinates of the intersection of the two lines are (x, y) = (7, -3).

Explanation:

To find the coordinates of the intersection of the two lines represented by the equations 2x + 3y = 5 and 3x + y = 18, we can solve this system of linear equations. Here's how to proceed step-by-step:
Step 1: Label the equations.
Let's call the first equation (1) and the second equation (2) for easy reference.
(1) 2x + 3y = 5
(2) 3x + y = 18
Step 2: Solve one of the equations for one of the variables.
Let's solve equation (2) for y:
y = 18 - 3x
Step 3: Substitute the expression for y in equation (1).
Now we substitute y in equation (1) with the expression we got from equation (2):
2x + 3(18 - 3x) = 5
Simplify the equation:
2x + 54 - 9x = 5
Combine like terms:
-7x + 54 = 5
Step 4: Simplify the equation for x.
Now we isolate x:
-7x = 5 - 54
-7x = -49
Divide both sides by -7 to find x:
x = -49 / -7
x = 7
Step 5: Substitute the value of x back into the equation for y.
We already have the expression for y from step 2 which was y = 18 - 3x. Now we substitute x = 7 into this expression to get y:
y = 18 - 3(7)
y = 18 - 21
y = -3
Step 6: State the coordinates of the intersection.
The coordinates of the intersection of the two lines are (x, y) = (7, -3).
Therefore, the vertex of the triangle at the intersection of the two graphs is at the point (7, -3).