3. Solve the system of equations. Show your work. y = x^2-3x+4 x + y = 4

Answer:

sin(B)=cos(90°-B)

Step-by-step explanation:

we know that

In the right triangle of the figure

sin(B)=b/c -----> The sine of angle B is equal to divide the opposite side to angle B by the hypotenuse

cos(A)=b/c -----> The cosine of angle A is equal to divide the adjacent side to angle A by the hypotenuse

we have that

sin(B)=cos(A)

Remember that

A+B=90° -----> by complementary angles

so

A=90°-B

therefore

sin(B)=cos(A)

sin(B)=cos(90°-B)

Answer:

sin(B) = cos(90 -B)

Step-by-step explanation:

In triangle ABC by using angle sum property, ∠A + ∠B + ∠C= 180°

∠A + ∠B + 90°= 180°

∠A + ∠B= 180°-90°

∠A + ∠B = 90°

∠A = 90°- ∠B

sin B = b/a.

cos A = b/a.

Hence, sin B = cos A

put the value of ∠A = 90°- ∠B in cos A

sin (B) = cos (90°-B)

Thus, the correct answer is option (2).

Answer:

Step-by-step explanation:

that would be written as  1.2^10, and the end result would be the same as you'd get if you use 1.2 as a factor 10 times:  1.2*1.2*1.2* .......1.2

You could use a calculator to evaluate 1.2^10:  

Typing in 1.2^10, you'll get  6.191736422.

This is not an exact answer; there are more digits following the ones shown.

Another way in which you could do this problem would be to use logs:

Let y = 1.2^10.  Then log y = 10*log 1.2, or log y = 10(0.07918) = 0.791812.

Finding the antilog, we get y = 6.19174

Answer:

Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

Step-by-step explanation:

Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.  

The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

Answer: Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction so the answer is B

Step-by-step explanation:

Answer:

C. AB/XY = AC/XZ

Step-by-step explanation:

Dilation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The original figure either stretches or shrinks by a certain factor.

In the problem, the dilation is by a factor of 5 and we can see that ABC shrinks to form XYZ.

So, ABC and XYZ are similar triangles which means that the ratio of their corresponding sides will be equal:

AB/XY = AC/XZ = BC/YZ = 5

Answer with explanation:

When ΔABC is dilated by a Scale factor of 5 we will get ΔX Y Z.

Pre-Image = ΔABC

Image = ΔX Y Z

When a triangle is dilated , then the two Triangles that is Original ΔABC and Triangle after dilation ΔX Y Z will be Similar.

⇒Similar triangles has Corresponding sides proportional as well as Corresponding  Angles are congruent.

≡Corresponding congruent Angles are

→∠A=∠X

→∠B=∠Y

→∠C=∠Z

≡Corresponding congruent Sides are

     [tex]\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}[/tex]

The Proportionality statement which proves two triangles are Similar

Option B

 [tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]

[tex]\bf \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 3^{x+1}=15\implies \log_{10}(3^{x+1})=\log_{10}(15)\implies (x+1)\log_{10}(3)=\log_{10}(15) \\\\\\ x+1=\cfrac{\log_{10}(15)}{\log_{10}(3)}\implies \stackrel{\textit{change of base rule}}{x=\cfrac{\log_{e}(15)}{\log_{e}(3)}-1}\implies x\approx 1.47[/tex]

Answer:

[tex]x=\frac{log(15)}{log(3)}-1[/tex]

Step-by-step explanation:

[tex]3^{x+1} = 15[/tex]

LEts convert exponential form to log form

[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]

WE apply the same rule to convert the given exponential form to log form

[tex]3^{x+1} = 15[/tex]

[tex]log_3{15} = x+1[/tex]

HEre the base of log is 3. Lets apply change of base formula

[tex]log_b(a)=\frac{log(a)}{log(b)}[/tex]

[tex]log_3{15} = x+1[/tex]

[tex]\frac{log(15)}{log(3)} = x+1[/tex]

Now subtract 1 from both sides

[tex]x=\frac{log(15)}{log(3)}-1[/tex]

For this case we have a function of the form [tex]y = g (x)[/tex]

Where:

[tex]g (x) = x ^ 2 + 2[/tex]

We must find the value of the function when x = 3. Then we substitute:

[tex]g (3) = 3 ^ 2 + 2\\g (3) = 9 + 2\\g (3) = 11[/tex]

Thus, the value of the function when [tex]x = 3[/tex] is [tex]y = 11[/tex]

Answer:

[tex]g (3) = 11[/tex]

Option C

Answer: Third Option

[tex]g(3) = 11[/tex]

Step-by-step explanation:

We have the function  [tex]g(x) = x^2 + 2[/tex] and we must find the value of g(3).

To find g (3) we must evaluate the function g(x) for x = 3. That is, we must replace x = 3 in the function

Then

[tex]g(x) = x^2 + 2[/tex]

[tex]g(3) = (3)^2 + 2[/tex]

[tex]g(3) = 9 + 2[/tex]

[tex]g(3) = 11[/tex]

Finally the correct answer is the third option

Answer:

∠C = 143°

Step-by-step explanation:

For the quadrilateral to be a parallelogram

Then ∠C = ∠A

Given ∠B = ∠D then consecutive angles are supplementary, that is

∠C + ∠D = 180

∠C + 37 = 180 ( subtract 37 from both sides )

∠C = 143°

Answer:

C) a= -1, b=5, c= -7

Step-by-step explanation:

To get the values of a, b and c we must first write the equation in the form

ax²+bx+c=0 where a b and c are the coefficients.

Therefore, -x² +5x=7 can also be written as:

-x²+5x-7=0

a= -1 ( coefficient of x²)

b=5 (coefficient of x)

c= -7 ( the constant in the equation)

Answer:

a=-1, b=5 and c=-7

Step-by-step explanation:

We have the following equation:

[tex]-x^{2} + 5x = 7[/tex] → [tex]-x^{2} + 5x - 7 = 0[/tex]

Given the equation of a parabola: [tex]ax^{2} +bx + c = 0[/tex]. By comparison, we know that:

a=-1, b=5 and c=-7

So the correct option is Option C.

Answer:

True.

Step-by-step explanation:

It's true.

The sin of 30 in degrees equals 1/2 and the cos of 30 degrees equals sqrt(3)/2.

I am attaching a table that can be useful for remembering the values of the cosine and sine of some angles.

Answer:

True

Step-by-step explanation:

Answer:

1/3 - 1/x=1/5

Step-by-step explanation:

Let the total work be "1"

                        Brody          Hudson              Brody+Hudson

  Time              3 mins            x min                       5 min

  Efficiency        1/3                   -1/x                          1/5

The efficiency of Hudson is negative as he is taking out the candies out of the bowl, since efficiency of Brody + efficiency of Hudson = efficiency of both, which means,

1/3 - 1/x = 1/5....

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+(y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) = (- 4,2)\\(x_ {2}, y_ {2}) = (1, -3)[/tex]

Substituting we have:

[tex]d = \sqrt {(1 - (- 4)) ^ 2+(-3-2) ^ 2}\\d = \sqrt {(1 + 4) ^ 2+(-5) ^ 2}\\d = \sqrt {(5) ^ 2+(-5) ^ 2}\\d = \sqrt {25 + 25}\\d = \sqrt {50}\\d = 7.07units[/tex]

Answer:

Option B

Answer: Option B

[tex]d=7.07[/tex]

Step-by-step explanation:

The distance between two points is calculated using the following formula

[tex]d=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}[/tex]

In this problem we have the following points

(-4,2) and (1,-3)

Therefore

[tex]x_0=-4\\y_0 = 2\\x_1=1\\y_1=-3[/tex]

Then the distance d is:

[tex]d=\sqrt{(1-(-4))^2+((-3)-2)^2}[/tex]

[tex]d=\sqrt{(1+4)^2+(-3-2)^2}[/tex]

[tex]d=\sqrt{(5)^2+(-5)^2}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=5\sqrt{2}[/tex]

[tex]d=7.07[/tex]

The correct answer is 1980 or A:)

Answer:

Step-by-step explanation:

[tex]\text{We have:}\\\\A_{PQRS}=45\ cm^2\\\\A_{PQRS}=a(7+b)\\\\A_{PXYS}=10\ cm^2\\\\A_{PXYS}=ab\\\\\text{Therefore we have the system of equations:}\\\\\left\{\begin{array}{ccc}a(7+b)=45&\text{use the distributive property}\\ab=10\end{array}\right\\\left\{\begin{array}{ccc}7a+ab=45&(1)\\ab=10&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\7a+10=45\qquad\text{subtract 10 from both sides}\\7a=35\qquad\text{divide both sides by 7}\\a=5\\\text{Put it to (2):}\\5b=10\qquad\text{divide both sides by 5}\\b=2[/tex]

Answer:

parallel

Step-by-step explanation:

we have

2x=-3-y

isolate the variable y

y=-2x-3 ----> equation A

4+y=-2x-2

isolate the variable y

y=-2x-2-4

y=-2x-6 -----> equation B

Remember that

If two lines are parallel, then their slopes are the same

Line A and Line B have the same slope m=-2 and different y-intercept

therefore

The lines are parallel

Answer:

Second option: Parallel.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

[tex]2x=-3-y \\\\2x+y=-3\\\\y=-2x-3[/tex]

Equation 2

[tex]4+y=-2x-2\\\\y=-2x-2-4\\\\y=-2x-6[/tex]

You can notice that the slope of the Equation 1 is:

[tex]m_1=-2[/tex]

And the slope of the Equation 2 is:

[tex]m_2=-2[/tex]

Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are: Parallel.

Answer:

A

Step-by-step explanation:

Just try to label the data in a table for every choice. It is clearly A. If you tried to solve it you will find that =

(-2)² = 4

(-1)² = 1

1² = 1

2² = 4

To perform F(g(x)), substitute g(x) into F(x) by squaring g(x) and subtracting 4. The domain of F(g(x)) is all real numbers.

The question asks us to perform the composition of two functions - f(x) and g(x). Composition is denoted by (f ∘ g)(x) and involves substituting the output of the inner function (g(x)) into the input of the outer function (f(x)). In this case, we have f(g(x)), which means we need to substitute g(x) into f(x).

First, substitute g(x) into f(x) to get f(g(x)):

f(g(x)) = (g(x))^2 - 4 = (x+2)^2 -4 = x^2 + 4x + 4 - 4 = x^2 + 4x.

The domain restriction is the set of all values that x can take. Since there are no restrictions mentioned in the question, the domain is all real numbers.

https://brainly.com/question/30143914

#SPJ12

Answer:

Step-by-step explanation:

-5 -3 ×2 /8

-11/8

Hence the answer is,

-11/8

Answer:

A. 24 square units

Step-by-step explanation:

length is 8 and height is 6

gets you 48 but you need to divide by 2 because its a triangle so you get 24

Answer:

a

Step-by-step explanation:

Answer:

A:  x-axis

I did a quiz and got it wrong when I choose B: y-axis.

Final answer:

The point with coordinates (0, 3) is on the y-axis, above the origin by 3 units. Therefore, the correct answer is B, the y-axis.

Explanation:

A point with the coordinates (0, 3) is located where the x-coordinate is 0 and the y-coordinate is 3. In the context of a two-dimensional Cartesian coordinate system, this means the point does not move left or right from the origin on the horizontal axis, but it moves up by 3 units on the vertical axis.

Therefore, the correct answer to the question is B, the point is located on the y-axis. It is neither on the x-axis nor in any of the four quadrants since its x-coordinate is zero. Hence, it lies directly above the origin on the y-axis.

Answer: 30

Step-by-step explanation: Start off by multiplying the two numbers.

3 x 10 = 30.

30 is a common multiple. Find any multiples below 30. Let’s start off using the biggest number of the two, which is 10, to see what other numbers can be multiples. 10, 20, and 30 can be. 3 can’t be divided into 10 or 20, so your least common multiple is 30.

Answer:

-59/17 =x

Step-by-step explanation:

53=-6-17x​

Add 6 to each side

53+6=-6+6-17x​

59 = -17x

Divide each side by -17

59/-17 = -17x/-17

59/-17 = x

-59/17 =x

The equation of f(x) is  B. F(x) = -√x. Therefore , B. F(x) = -√x is correct.

Here's why:

The parent function of the graph is the square root function, which means the original equation is f(x) = √x.

The graph is reflected across the x-axis.

This means that the y-values are multiplied by -1. In other words, if the original point was (x, √x), the reflected point would be (x, -√x).

Therefore, the equation of the reflected function is f(x) = -√x.

The other options are incorrect because:

A. F(x) = √x is the original equation, not the reflected equation.

C. F(x) = √x - 1 shifts the graph down one unit, but it does not reflect it across the x-axis.

D. F(x) = √x + 1 shifts the graph up one unit, but it does not reflect it across the x-axis.

Answer:

$24,000

Step-by-step explanation:

After putting in trust they have left:

48000 - 9600 = $38,400

If Tori gets 3/8, Akira will get the remaining (1 - 3/8 = 5/8). So Akira will get:

[tex]\frac{5}{8}*38,400=24,000[/tex]

Hence akira will get $24,000

Answer:

6 more than 5 times the measure of mn is (5mn + 6)

Step-by-step explanation:

Answer:

(x,y)  (2,-1)

Step-by-step explanation:

Answer:

the first one is 2 the second one is 3

Step-by-step explanation:

Answer:

The answer is 192

Step-by-step explanation:

2^8 = 256

8^2 = 64

256 - 64 = 192

Remember:

2^8 is really 2*2*2*2*2*2*2*2

Remember:

8^2 is really 8*8

To find the difference, you must subtract the smaller product from the larger product.

<Hope this helps!>

Answer:

192

Step-by-step explanation:

Method 1:

2^8 - 8^2 = 2^8 - 2^6 = 2^6(2^2 - 1) = 64(3) = 192

Method 2:

2^8 - 8^2 = 256 - 64 = 192

Answer:

(1/2)x+3/2

or

0.5x+1.5

Step-by-step explanation:

Hopefully you mean to have that dot between f and g closed because if it open it means something totally different.

So closed dot means multiplication

Open dot means you are composing a function with another one

So here you are just doing (x+3)  *  (1/2)

Just use distributive property   (1/2)x+(1/2)(3)

(1/2)x +3/2

or

0.5x+1.5

Answer:

The sequences are arithmetic

1).-8.6, -5.0, -1.4, 2.2, 5.8

2).  5, 1, -3, -7, -11

3). -3, 3, 9, 15, 21

Step-by-step explanation:

If a sequence is a an AP then there is a common difference d.

1) Check sequence 1

-8.6, -5.0, -1.4, 2.2, 5.8

-5.0 - - 8.6 = 3.6

-1.4 - -5.4 = 3.6  It is an AP

2) Check sequence 2

2, -2.2,2.42, -2.662, 2.9282

-2.2 - 2 = -4.2

-2.662 - 2.42 = -5.082 Not AP

Similarly AP sequences are

5, 1, -3, -7, -11

-3, 3, 9, 15, 21

The sequence that are arithmetic are as follows:

5, 1, -3, -7, -11.

-3, 3, 9, 15, 21

-8.6, - 5.0, -1.4, 2.2, 5.8

Arithmetic sequence is a list of numbers with a definite pattern. Therefore, let's find the sequence with a definite pattern.

5, 1, -3, -7, -11.

This is a sequence as it as a definite pattern. The value are reduced by 4. Therefore, the common difference is 4.

-3, 3, 9, 15, 21

This is a sequence because it has a common difference of 6.

-8.6, - 5.0, -1.4, 2.2, 5.8

This is a sequence because it has a common difference of 3.6.

learn more on sequence here: https://brainly.com/question/17627016

Answer:

tan(90 - A) = 1/tan(A) ⇒ last answer

Step-by-step explanation:

* Lets revise some important information for the right triangle

- In any right triangle

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

∵ The sum of the interior angles of any triangle is 180°

∵ m∠B = 90°

∴ m∠A + m∠C = 180° - 90° = 90°

- If the measure of angle A is x°

∴ The measure of angle C = 90° - x°

- tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB  ⇒(1)

- tan(C) = opposite/adjacent

∵ The opposite to ∠C is AB

∵ The adjacent to ∠C is BC

∴ tan(C) = AB/BC ⇒  (2)

- From (1) and (2)

∴ tan(A) = 1/tan(C)

∵ m∠A = A , m∠C = (90 - A)

∴ tan(A) = 1/tan(90 - A)

OR

∴ tan(90 - A) = 1/tan(A)

Answer:

LAST OPTION.

Step-by-step explanation:

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

[tex]\frac{cos(x)}{sin(x)}=cot(x)=\frac{1}{tan(x)}[/tex]

[tex]sin(x\±y) = sin(x)cos(y)\±cos(x)sin(y)\\\\cos(x\±y) =cos(x)cos(y)\± sin(x)sin (y) [/tex]

[tex]sin(90\°)=1\\cos(90\°)=0[/tex]

Then, you need to rewrite [tex]tan(90-A)[/tex]:

[tex]tan(90-A)=\frac{sin(90-A)}{cos(90-A)}[/tex]

Applying the identities, you get:

[tex]tan(90\°-A)=\frac{sin(90\°)cos(A)-cos(90\°)sin(A)}{cos(90\°)cos(A)-sin(90\°)sin(A))}[/tex]

Finally, you must simplify. Then:

[tex]tan(90\°-A)=\frac{(1)cos(A)-(0)sin(A)}{(0)cos(A)-(1)sin(A))}\\\\tan(90\°-A)=\frac{cos(A)}{sin(A)}\\\\tan(90\°-A)=\frac{1}{tan(A)}[/tex]

Answer:

No, Lorena cannot make the inference about all the seniors going to college.

Step-by-step explanation:

We are given that Lorena took a survey of students in her science class to determine how many of them were going to college.

From the survey results, she found that 85% of the students from her science class were going to the college but with these results she cannot infer that 85% of all the seniors at her school were going to college.

This is because the survey was biased as it was not taken from the entire school but only Lorena's science class.

Answer:

No, Lorena’s sample was biased because it was taken only from an honors class.

No, Lorena’s sample was not a random sample of the entire school.

those are the two correct answers, i took the test!