40 POINTS

The sides of an isosceles triangle are 5, 5, and 7. Find the measure of the vertex angle to the nearest degree.

Answer:

16

Step-by-step explanation:

If you have a 12-inch board and you are making 3/4 inch long sections, and you want to know many times you can do that here.

You just need to take 12 and divide it by the 3/4, to see how many sections you can have.

[tex]12 \div \frac{3}{4}[/tex]

Change division to multiplication by taking the reciprocal (the flipping) of the second number:

[tex]12 \cdot \frac{4}{3}[/tex]

Write 12 as a fraction:

[tex]\frac{12}{1}\cdot \frac{4}{3}[/tex]

To multiply fractions, multiply straight across on top and straight across on bottom:

[tex]\frac{(12)(4)}{(1)(3)}[/tex]

[tex]\frac{48}{3}[/tex]

16

Final answer:

By dividing the 12-inch board length by the section length of 3/4 inches, we find that 16 sections can be made.

Explanation:

The question asks how many sections of 3/4 inches can be made from a 12-inch board. To find this, divide the total length of the board by the length of each section. Calculate by dividing 12 inches by 3/4 inches (which is the same as 12 divided by 0.75 in decimal form).

Therefore, you can cut 16 sections that are 3/4 inches long each from a 12-inch board.

Step-by-step explanation:

the correct answer is c

Answer:

512 is a perfect cube.

Step-by-step explanation:

because 8*8*8=512

The numbers are 10 and 3.

Step-by-step explanation:

STEP 1: Based on the problem, two equations can be set up:

First, "one number is seven less than another." This can be expressed mathematically:

Let x = first number

      y = second number

[tex]x \ - 7 = \ y[/tex]

The second equation is based on "their sum is thirteen."

[tex]x \ + \ y \ = 13[/tex]

STEP 2: Solve for the variables.

In this step, substitute the value of y from Equation 1 into Equation 2:

[tex]x \ + \ (x \ - \ 7) \ = \ 13\\2x \ - \ 7 \ = 13\\[/tex]

Next, solve for x by manipulating the equation:

[tex]2x \ = \ 13 \ + \ 7\\2x \ = \ 20\\\boxed {x \ = \ 10}[/tex]

Now that the value of x is known, it can be used to determine the value of y.

To do this, use the calculated value for x and plug it into Equation 1:

[tex]y \ = \ x \ - 7\\y \ = 10 \ - 7\\\boxed {y = \ 3}[/tex]

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Keywords: two equations, two variables

To find the two numbers where one is seven less than the other and their sum is thirteen, a system of equations is set up and solved, revealing that the only possible combination is 10 (larger number) and 3 (smaller number).

To solve the problem where one number is seven less than another and their sum is thirteen, let's set up some equations.

Let x be the larger number and y be the smaller number. We can express the two conditions in the following way:

y = x - 7  (the smaller number is seven less than the larger number)

x + y = 13 (their sum is thirteen)

Substituting the first equation into the second gives us:

x + (x - 7) = 13

Simplifying, we get:

2x - 7 = 13

Adding 7 to both sides, we have:

2x = 20

Dividing both sides by 2, we find:

x = 10

Now we substitute x back into the first equation to find y:

y = 10 - 7

y = 3

So the larger number is 10 and the smaller number is 3. There is only one possible combination of numbers that fit the given conditions.

Answer:

The standard equation is x²/16 + y²/49 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with  

   center (0 , 0) is x²/b² + y²/a² = 1 , where  

* The coordinates of the vertices are (0 , ± a)  

* The coordinates of the foci are (0 , ± c), where c² = a² - b²  

* Now lets solve the problem

∵ The vertices of the ellipse are (0 , -7) , (0 , 7)

∵ The coordinates of the vertices are (0 , - a) , (0 , a)

∴ a = 7 , -7

∵ The coordinates of the foci are (0 , -√33) , (0 , √33)

 ∵ The coordinates of the foci are (0 , - c) , (0 , c)

∴ c = -√33 , √33

∵ c² = a² - b²

∵ a² = (7)² = 49

∵ c² = (√33)² = 33

∴ 33 = 49 - b² ⇒ subtract 49 from both sides

∴ -16 = -b² ⇒ multiply both sides by -1

∴ b² = 16

∵ The standard equation of the ellipse is x²/b² + y²/a² = 1

∴ The standard equation is x²/16 + y²/49 = 1

Answer:

Slope is [tex]\frac{1}{3}[/tex]

Good job on the y-intercept!

[tex]f(x)=\frac{1}{3}x+3[/tex] is function represented here.

Step-by-step explanation:

The slope is [tex]\frac{\text{rise}}{\text{run}}[/tex].

Let's start at the left dot on your screen; we are going to figure out how to get to (0,3) only using up, down,right, left.

So since the slope is [tex]\frac{\text{rise}}{\text{run}}[/tex] and we are starting at the left dot trying to get to right, let's find the rise part first.  How much would you need to rise to get on the same level as that dot on the right? You should say the rise is positive 1 (since you go up 1).

Now that we are on the level, what would you need to run from left to right to get to the right dot.  The run is positive 3 (since we went right 3).

So the slope is  [tex]\frac{\text{rise}}{\text{run}}=\frac{1}{3}[/tex]

You did good on the y-intercept! Good job!

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

[tex]m=\frac{1}{3}[/tex] and [tex]b=3[/tex]

Plug this in:

[tex]y=\frac{1}{3}x+3[/tex]

Answer:

(-1,4) This is the solution for the given system

Step-by-step explanation:

The first graph is shown in the first picture attached, it has the points (3,0) and (0,3)

The other graph is attached as well

The solution for this system is the interception between the graph

Answer:

3^x -2x +14

Step-by-step explanation:

I will assume you mean 3^x in the function f(x)

f(x) = 3^x+ 10

g(x) = 2x - 4

(f - g)(x) =  3^x+ 10  - (2x - 4)

       Distribute the minus sign

              =  3^x+ 10  - 2x + 4

              = 3^x -2x +14

Answer:

C. 5√3

Step-by-step explanation:

To figure this out, we need to apply the Pythagorean Theorem, a² + b² = c², where c is the "HYPOTENUSE". In this case, c is already found for us [10], so the operation we use whenever the hypotenuse is defined is deduction, or subtraction. Apply the Pythagorean Theorem: a² + 25 = 100; 75 = a². Now, to find a, we need to find two numbers that multiply to 75, where one of them is a PERFECT SQUARE, and in this case, they are 3 and 25. Since the square root of 25 is 5 [in this case, NO NON-NEGATIVE root], that gets moved to the outside of the radical, and 3 [NON-PERFECT SQUARE] stays wrapped under the radical, ending up with 5√3. You understand?

I am joyous to assist you anytime.

Answer:

A

Step-by-step explanation:

To solve the equation 4.25x = 21, divide both sides by 4.25 to isolate x, resulting in x = 4.94 (rounded to two decimal places).

To solve for x in the equation 4.25x = 21, we need to isolate x by performing the following steps:

Therefore, the solution to the equation is x = 4.94.

Before the translation, the coordinates of C are (-1, 2).

If we translate C 3 to the left, it becomes (-1 - 3, 2), or (-4, 2).

If we translate C 9 down, it becomes (-4, 2 - 9), or (-4, -7).

Therefore, the coordinates of C' would be (-4, -7).

Hope this helps! :)

The requried coordinates of the translated point C' are (-4, -7). Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,

The coordinates of point C before translation are (-1, 2). If we move point C 3 units to the left, its new coordinates would be (-1 - 3, 2), or (-4, 2). If we then move point C 9 units down, its new coordinates would be (-4, 2 - 9), or (-4, -7).

Therefore, the coordinates of the translated point C' are (-4, -7).

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Answer:

you can use it in architecture and construction

Step-by-step explanation:

say you are building a sloped roof. If you know the height of the roof and the length for it to cover, you can use the Pythagorean Theorem to find the diagonal length of the roof's slope. You can use this information to cut properly sized beams to support the roof, or calculate the area of the roof that you would need to shingle. I hope this helps!

Two different real-life examples of world situations to represent the Pythagorean theorems are:

"Pythagoras theorem is defined as in the right-angled triangle square of the hypotenuse is equals to the sum of the square of other two sides."

According to the question,

Two different real-life examples of world situations to represent the Pythagorean theorems are:

   2. The height of the original tree using the length of a broken tree      

        lying on itself touching the ground: broken part represents the

        hypotenuse, the ground represents the base, and the left part of  

          the tree is the perpendicular side.

Hence, two different real-life examples of world situations to represent the Pythagorean theorems are:

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Answer:

163

Step-by-step explanation:

0 judges - [tex]C^8_0=1[/tex] way to vote

1 judge - [tex]C^8_1=8[/tex] ways to vote

2 judges-

[tex]C^8_2=\dfrac{8!}{2!(8-2)!}=\dfrac{6!\cdot 7\cdot 8}{2\cdot 6!}=\dfrac{56}{2}=28[/tex]

ways to vote for 2 different judges

3 judges-

[tex]C^8_3=\dfrac{8!}{3!(8-3)!}=\dfrac{5!\cdot 6\cdot 7\cdot 8}{2\cdot 3\cdot 5!}=\dfrac{6\cdot 56}{6}=56[/tex]

ways to vote for 3 different judges

4 judges-

[tex]C^8_4=\dfrac{8!}{4!(8-4)!}=\dfrac{4!\cdot 5\cdot 6\cdot 7\cdot 8}{4!\cdot 4!}=\dfrac{5\cdot 6\cdot 7\cdot 8}{2\cdot 3\cdot 4}=5\cdot 7\cdot 2=70[/tex]

ways to vote for 4 different judges

In total, there are

[tex]1+8+28+56+70=163[/tex]

different ways to vote.

Answer:

Part 1) The area of the base of the rectangular prism is [tex]18\ cm^{2}[/tex]

Part 2) The height of the rectangular prism is equal to [tex]6\ cm[/tex]

Part 3) The volume of the rectangular prism is [tex]108\ cm^{3}[/tex]

Step-by-step explanation:

Part 1) What is the area of the base of the rectangular prism?

we know that

The base of the rectangular prism is the rectangle ABCD

so

AD=BC and AB=DC

The area B of the rectangle is equal to

[tex]B=AD*DC[/tex]

substitute

[tex]B=(9)(2)=18\ cm^{2}[/tex]

Part 2) What is the height of the rectangular prism?

The height of the rectangular prism is equal to the segment line AW (segment perpendicular to the base)

we have that

[tex]H=AW=BX=DY=CZ=6\ cm[/tex]

Part 3) What is the volume of the rectangular prism?

we know that

The volume of the rectangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base of the prism

H is the height of the prism

we have

[tex]B=18\ cm^{2}[/tex]

[tex]H=6\ cm[/tex]

substitute

[tex]V=(18)(6)=108\ cm^{3}[/tex]

The area of the base of the rectangular prism is 18 cm² and its volume is 108 cm³.

Prism is a three dimensional shape with two identical shapes called bases facing each other.

From the diagram:

Area of base = length * width = 9 cm * 2 cm = 18 cm²

Volume = height * length * width = 6 * 9 * 2 = 108 cm³

The area of the base of the rectangular prism is 18 cm² and its volume is 108 cm³.

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The solution of the given inequality is (- √5) ≤ x ≤ (+√5).

"An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. "

The given inequality is:

x² - 5 ≤ 0

⇒ x² ≤ 5

⇒ x ≤ (± √5)

Therefore, the solution is (- √5) ≤ x ≤ (+√5).

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Answer:

15-8  

HOPE THIS HELP

Step-by-step explanation:

Answer:

15 - 8i

Step-by-step explanation:

5√9-√(-64) = ?  Rewrite -√(-64) as -8i.

Then we have 5(3) - 8i, or 15 - 8i.

Answer:

[tex]6.180 \cdot 10^{-5}[/tex]

Step-by-step explanation:

So I'm going to separate the fraction like so:

[tex]\frac{3.3 \cdot 10^2}{5.34 \cdot 10^6}=\frac{3.3}{5.34} \cdot \frac{10^2}{10^6}[/tex]

I'm going to do the 3.3 divided by 5.34 in my calculator.

3.3/5.34 is equal to 0.6179775 (approximately).

I'm going to use law of exponents to simplify: [tex]\frac{10^2}{10^6}[/tex].

When you are dividing by the same based number, you subtract the exponents. So you will keep the same based number and your exponent will be top exponent minus bottom exponent. Like this:

[tex]\frac{10^2}{10^6}=10^{2-6}=10^{-4}[/tex].

So this is what we have right now before moving on.

The answer is approximately [tex]0.6179775 \cdot 10^{-4}[/tex].

In order for this to be in scientific notation we need the first number to be between 1 and 10 (not including 10). To do this, we move the decimal either left or right depending where it is and change the factor of 10.

So 0.6179775 only needs to have the decimal moved over once to the right so 0.6179775 is [tex]6.179775 \cdot 10^{-1}[/tex]

The exponent of -1 came form us moving it right once.

So now this is what we have so far:

[tex]6.179775 \cdot 10^{-1} \cdot 10^{-4}[/tex]

I brought down the 10^(-4) form earlier because I was focusing on the the other part to be in scientific notation.

So if you have the same based number when multiplying, you add the exponents like so:

[tex]6.179775 \cdot 10^{-1+-4}[/tex]

[tex]6.179775 \cdot 10^{-5}[/tex]

Now I didn't worry about the 4 significant digits until now.

We want the first 4 digits reading the number from left to right on our first number.

[tex]6.180 \cdot 10^{-5}[/tex]

I rounded because the 5th digit was 5 or more.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}\dfrac{1}{3}x+\dfrac{1}{4}y=1&\text{multiply both sides by 12}\\2x-3y=-30\end{array}\right\\\left\{\begin{array}{ccc}12\!\!\!\!\!\diagup^4\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+12\!\!\!\!\!\diagup^3\cdot\dfrac{1}{4\!\!\!\!\diagup_1}y=12\cdot1\\2x-3y=-30\end{array}\right\\\left\{\begin{array}{ccc}4x+3y=12\\2x-3y=-30&\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x+3y=12\\-4x+6y=60\end{array}\right}\qquad\text{add both sides of the equations}[/tex]

[tex].\qquad9y=72\qquad\text{divide both sides by 9}\\.\qquad y=8[/tex]

Answer:

8

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

If B = blue bikes

sum = addition

and 9 = red bikes

so B+9

Answer:

(-2,6)

Step-by-step explanation:

If b is (6,4) and we have b' is the image that follows from the translation

(x-8,y+2).

Basically the image of (x,y) is (x-8,y+2).

So the image of (6,4) is (6-8,4+2).

Simplify:

(6-8,4+2)

(-2,6).

b' is (-2,6).

Answer:

Radius r = ±√52

Coordinates of center =

Step-by-step explanation:

Points to remember

Equation of a circle passing through the point (x1, y1) and radius r is given by

(x - x1)² + (y - y1)² = r ²

To find the radius  and coordinates of center

It is given that an equation of circle,

(x - 4)² + (y + 6)² = 52

Compare two equations,

we get  r ²  = 52

r = ±√52

(x - x1)²  = (x - 4)²  then x1 = 4

(y - y1)² = (y + 6)² then  y1 = -6

Coordinates of center = (4, -6)

Answer:

(x − 4)2 + (y + 6)2 = 25

(x − 4)2 + (y − (-6))2 = 52

When I compare my equation with the standard form, (x − h)2 + (y − k)2 = r2, I get h = 4, k = -6, and r = 5. The center is at (4, -6), and the length of the radius is 5.

Step-by-step explanation:

Plato :)

Answer:

y = - x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = - 1 and y- intercept c = - 5, hence

y = - x - 5 ← equation of line

Answer:

The answer is 6x^2-2x-10

Step-by-step explanation:

(4x2 + 5x - 7) + (2x2 - 7x - 3)

This is an addition question:

First step is open the parenthesis

4x2 + 5x - 7 + 2x2 - 7x - 3

Arrange the terms according to the exponents:

4x^2+2x^2-7x+5x-7-3

Solve the like terms:

6x^2-2x-10

Thus the answer is 6x^2-2x-10 ....

[tex](4 {x}^{2} + 5x - 7) + (2 {x}^{2} - 7x - 3) \\ \\ open \: the \: brackets \\ \\ 4 {x}^{2} + 5x - 7 + 2 {x}^{2} - 7x - 3 \\ \\ 6 {x}^{2} - 2x - 10[/tex]

While opening the brackets, make sure you change the signs accordingly.

Hope it helps!

The diagonal AC can be considered a transversal to the CD and AB of tht parallelogram ABCD

The measure of ∠DAC is 34°

Reason:

The given parameters;

ABCD is a parallelogram; Given

AC is a diagonal of parallelogram ABCD; Given

m∠CAB = 21°, and m∠ADC = 125°; Given

We have;

m∠CAB ≅ m∠ACD by alternate interior angles theorem

∴ m∠CAB = m∠ACD = 21°

m∠ACD + m∠ADC + m∠DAC = 180°

m∠DAC = 180° - (m∠ACD + m∠ADC)

∴ m∠DAC = 180° - (21° + 125°) = 34°

The measure of ∠DAC = 34°

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Answer:

Option A.

Step-by-step explanation:

In the given triangles XYZ and ACB,

∠X ≅ ∠A ≅ 90°

∠Z ≅ ∠C

And ∠Y ≅ ∠B

Measures of the corresponding angles in the given triangles XYZ and ACB are same.

Therefore, ΔXZY ≅ ΔACB

[We will write the corresponding angles of ΔABC in the same order as given for ΔXZY.]

Option A. will be the correct option.

Answer: it is abc

Step-by-step explanation:

Answer:

27/35

Step-by-step explanation:

(f/g)(5) means f(5)/g(5).

So we will need to find both f(5) and g(5).

f(5) means replace x with 5 in f. This gives us 7+4×5.

Let's simplify 7+4×5:

7+4×5

7+20

27.

g(5) means replace x with 5 in g. This gives us 7×5.

Simplifying 7×5 gives us 35.

(f/g)(5)=f(5)/g(5)=27/35.

Answer:

[tex]\sin(\frac{\pi}{7}+x)[/tex]

Step-by-step explanation:

We are going to use the identity

[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]

because this identities right hand side matches your expression where

[tex]a=\frac{\pi}{7}[/tex] and [tex]b=x[/tex].

So we have that [tex]\sin(\frac{\pi}{7})\cos(x)+\cos(\frac{\pi}{7})\sin(x)[/tex] is equal to [tex]\sin(\frac{\pi}{7}+x)[/tex].

The given expression is written as sin(π/7 + x). Using sine of compound angle identity it is obtained.

A compound angle is the sum of two or more angles. Consider A and B are two angles. Where their compound angle becomes A + B. So, the sine and cosine of this compound angle are

1) sin (A + B) = sin A cos B + cos A sin B

2) sin (A - B) = sin A cos B - cos A sin B

3) cos (A + B) = cos A cos B - sin A sin B

4) cos (A - B) = cos A cos B + sin A sin B

The given expression is sin(π/7) cos(x) + cos(π/7) sin(x)

This is in the form of sin A cos B + cos A sin B

where A = π/7 and B = x

So, using the above identity we can write,

sin(π/7) cos(x) + cos(π/7) sin(x) = sin(π/7 + x)

Thus, the given expression is expressed in the angle of sine. I.e., sin(π/7 + x).

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Answer:

C: 12.5

Step-by-step explanation:

The sides x and 11 could be defined as the Adjacent angle and the Hypotenuse. This means that we will use the cos function to solve this.

First we can set up our equation

[tex]cos28=\frac{11}{x}[/tex]

Next we can solve for x by multiplying by x and dividing by [tex]cos 28[/tex]

[tex]x=\frac{11}{cos28}\\\\x=12.458\\\\x=12.5[/tex]

Answer:

c 12.5

Step-by-step explanation:

cos 28 = adjacent side/ hypotenuse

cos 28 = 11/x

Multiply each side by x

x cos 28 = 11/x *x

x cos 28 = 11

Divide each side by cos 28

x cos 28/ cos 28 =11 /cos 28

x = 11 /cos 28

x =12.45827056

To the nearest tenth

x = 12.5

When we have dependent and independent variables we will have a linear relationship.

Let x be the independent variable and y be the dependent variable.

To write the  relationship we will have :

y = kx + c

Where k and c are constants.

In the case of a line the constant k is the gradient.

A multiplicative change is a log form and it is given by :

Y = Ck^x

The relationship is not linear but exponential.

The correct answer is thus :

Additive rate of change.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

========================================

We have the points (-1, -4) and (1, 6). Substitute:

[tex]m=\dfrac{6-(-4)}{1-(-1)}=\dfrac{10}{2}=5[/tex]

[tex]y-(-4)=5(x-(-1))\\\\y+4=5(x+1)[/tex]

Convert it to the standard form [tex]Ax+By=C[/tex]:

[tex]y+4=5(x+1)[/tex]          use the distributive property

[tex]y+4=5x+5[/tex]         subtract 4 from both sides

[tex]y=5x+1[/tex]           subtract 5x from both sides

[tex]-5x+y=1[/tex]        change the signs

[tex]5x-y=-1[/tex]