(20 points) what is 4x^2 = 32 ?

The answer is -2

Sure hope this helps you

The number of students that are expected to carry a backpack is = 378

The total number of students in the assembly= 648

The number of students that enters the gym =12

The number of students carrying backpack = 7 out of 12

The total number of batches that entered the gym = 648/12 = 54

Therefore, the number of students that are expected to carry a backpack is = 54 ×7 = 378

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The cosine is the ratio of hypotenuse and base. Then the measure of the angle ∠L will be 60°.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The right-angle triangle is given below.

The length of the hypotenuse is 16 and the base length is 5.

Then the measure of the angle ∠L will be

cos L = 5 / 10

cos L = 1 / 2

      L = cos⁻¹ (1 / 2)

      L = 60°

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For the function: y = x² + 4

For the function: x² - 4

For the function: 1 - x²

Conclusion:

green line = x² + 4;  blue line = x² - 4; black line = 1 -x²

Answer:

See below ~

Step-by-step explanation:

Equation of Graph A :

Equation of Graph B :

Equation of Graph C :

Answer:

248

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary.

56 + y = 180

y = 180-56

y =124

The opposite angles of a parallelogram are equal.

x = y = 124

x+y = 124+124

      =248

Answer:

x + y = 248

Step-by-step explanation:

consecutive angles in a parallelogram sum to 180°

opposite angles are congruent

x + 56° = 180° ( subtract 56° from both sides )

x = 124°

then

y = x = 124 , so

x + y = 124 + 124 = 248

Answer:

= 240√3-3√3x

Step-by-step explanation:

parentheses:

=3√3 (80 – x)

Apply the distributive law:

a=3√3, b= 80, c =X

=3√3×80-3√3x

=3× 80√3 -3√3x

Multiply the numbers: 3×80 = 240

= 240√3-3√3x

Using sampling concepts, it is found that the population and the sample are given by:

Population: all the chicken meat; Sample: three random places in the chicken.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population.

In this problem, a group of 3 chicken meat is taken from all the chicken meat, which is the population, hence the correct option is given by:

Population: all the chicken meat; Sample: three random places in the chicken.

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Rina Take home pay is $457.20

The basic salary divided by the Gross salary is multiplied by 100. The result is the percentage of gross salary.

Given that:

gross salary = $624

14% income tax = 624* 0.14 = $87.36

group health plan = $4.25

Company retirement = 624 * 0.060 =$37.44

Social Security = 624 * 0.0605 = $37.752

Home pay= 624 - 87.36 - 4.25 - 37.44- 37.752

= 457.198

Her take home pay is $457.198

if she gets a $35 raise per pay period,

So, new gross salary would be,

= $624 + $35

= $659.

Again, we have

14% Income tax = 659 * 0.14 = $92.26

Group health plan = $4.25

Company retirement = 659 * 0.060 = $39.54

Social Security = 695* 0.0605  = $39.8695

Home take pay,

=659-39.8695 - 45.825 - 39.54-92.26

=441.5055

Her take home pay is $441.5055

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Answer:

43.43

Step-by-step explanation:

Convert 25 minutes to decimal degrees by 25/60 = 0.416...=0.42

Convert 36 seconds to decimal degrees by 36/3600 (There are 3600 seconds in a degree) = 0.01

Now you have:

43 degrees, 0.42 degrees. and 0.01 degrees.

Add them all to get 43.43

Answer:

379 (Rounded to nearest whole)

A = a² + 2a [tex]\sqrt{\frac{a^2}{4} + h^2}[/tex]

    = 10² + 2 × 10 × [tex]\sqrt{\frac{10^2}{4} + 13^2 }[/tex] ≈ 378.57

Answer:

Given:

Solution:

Let's assume Width of rectangle be x and Length of rectangle be x + 7 respectively.

Using formula

[tex] \\ \: \: \: \: \pink{ \dashrightarrow \: \: \: \: \sf { \underbrace{Area_{(Rectangle)} = Length × Width }}} \\ \\ [/tex]

On Substituting the required values, we get;

[tex]\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x)(x + 7) = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x = 744 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 7x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf {x}^{2} + 31x - 24x - 744 = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x(x + 31) - 24 (x + 31) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf (x + 31)(x - 24) = 0 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf x = 24 \: or \: - 31 \\ \\ [/tex]

As we know that width of the rectangle can't be negative. So x = 24

Hence,

[tex] \therefore[/tex]Length of rectangle is 31 yards and Width is 24 yards.

Answer:

[tex]2\sqrt{14}[/tex]

Step-by-step explanation:

To find, do 9^2-5^2=[tex]\sqrt{x\\}[/tex], so 81-25=56 which is 2[tex]\sqrt{14}[/tex]

Answer:

[tex]2\sqrt{14}[/tex]

Step-by-step explanation:

The missing side must be [tex]2\sqrt{14}[/tex] for the Pythagorean Theorem to be true.

Hope it helps, have a fantastic day.

Step-by-step explanation:

it does not matter, if you understand the equation itself. look at the graph ! what is the curve doing ?

I don't know the options of the pull-down menus, so I will give you my best guesses based on the facts :

the domain of a function is the set or interval of all valid x (or input) values.

the range of a function is the set of interval of all valid y (or functional result) values.

so, clearly, x is in the interval (-infinity, +infinity). which is therefore the domain.

please conduct the round brackets. they indicate that the specified interval limits are not included (as infinity is not a value, only a concept, and can never be reached).

and y is in the interval of (0, +infinity). which is therefore the range.

we have to use the round brackets also for 0, as the function will never deliver the value 0, but its tendency or limit goes there (but again, only in infinity, which will never be reached).

the function continuously decreases when x increases.

again, I am not sure what the options are here, and what your teacher wants to "hear".

The future value after 4 years will be $8156.49 if the value of the car today is $13,000 but will lose 11% of its value each year for the next several years.

Based on an estimated growth rate, the future value is the amount that an asset will be valued at a future date. The computation assumes that at the start date, a fixed amount of cash is made available for investment and that it increases at a constant rate until the selected future date.

We have:

Current value of the car = $13,000

Depreciation rate = 11%

Time n = 4 years

[tex]\rm Future \ value = (value \ at \ present) ( 1- \dfrac{depreciation \ rate}{100})^n[/tex]

[tex]\rm Future \ value = (13000)(1-\frac{11}{100} )^4[/tex]

Future value = $8156.49

Thus, the future value after 4 years will be $8156.49 if the value of the car today is $13,000 but will lose 11% of its value each year for the next several years.

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Answer:

Two right angles = 180 degrees

Step-by-step explanation:

A right angle = 90 degrees

The sum of the interior angles of a triangle = 180 degrees

Two right angles (2 * 90) = 180

180 = 180

Therefore, the sum of the interior angles of  any triangle is equal to two right angles.

Answer:

7662247+20728678=28290925+33807580=620985505

Answer:

Біологічні відносини є результатом взаємодії організмів один з одним. У природі немає організмів, які ізольовані від оточуючого середовища.

Missing: Проект ‎призи ‎нація (

the answer is 17,202 feet

The bird (B) from its nest (N) is 17202 ft.

Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.

This is very obviously a right triangle problem.

Side BO is the hypotenuse of the triangle, measuring 21000.

Side BN is the side adjacent to the given angle B, 35 degrees.

This is the cosine ratio:

cos∅ = adj/hyp

substitute the values

cos35° = x/21000 and solving for x:

21000.cos(35°) = x

x = 17202.19 or, rounded as we need:

x = 17202

Hence, the bird (B) from its nest (N) is 17202 ft

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According to "Black Hole Beginnings," the destruction of some stars results in an an intense gravitational pull.

To answer the question, we need to know what Black Holes are.

Blackholes are regions of space in which no matter can escape

So, when black holes are formed, some stars are destroyed and collapse due to intense gravitational forces.

So, according to "Black Hole Beginnings," the destruction of some stars results in an an intense gravitational pull.

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Answer:

the ans is c

Step-by-step explanation:ive done it b4

Answer:

z = 7/3 is extraneous.

Step-by-step explanation:

√(z^2+8) = 1 - 2z

z^2 + 8 = (1 - 2z)^2

z^2 + 8 = 1 -4z + 4z^2

3z^2 - 4z - 7 = 0

3z^2 + 3z - 7z - 7 = 0

3z(z + 1) - 7(z + 1) = 0

(3z - 7)(z + 1) = 0

3z = 7, z = -1

z = 7/3, -1.

One of these might be extraneous.

Checking:

√(z^2+8) = 1 - 2z, if z = -1:

√(1 + 8) = 3, -3

1 - 2(-1) = 3.    So its not z = -1

if z = 7/3

√((7/3)^2 + 8) = 13.44

1 - 2(7/3) = -3.66

So its z = 7/3

Answer:

[tex]z=\dfrac{7}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{z^2+8}=1-2z[/tex]

Square both sides:

[tex]\implies (\sqrt{z^2+8})^2=(1-2z)^2[/tex]

[tex]\implies z^2+8=1-4z+4z^2[/tex]

Subtract [tex]z^2[/tex] from both sides:

[tex]\implies 8=1-4z+3z^2[/tex]

Subtract 8 from both sides:

[tex]\implies 0=-7-4z+3z^2[/tex]

[tex]\implies 3z^2-4z-7=0[/tex]

Rewrite the middle term:

[tex]\implies 3z^2+3z-7z-7=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 3z(z+1)-7(z+1)=0[/tex]

Factor out the common term [tex](z+1)[/tex]:

[tex]\implies (3z-7)(z+1)=0[/tex]

Therefore:

[tex]\implies (z+1)=0 \implies z=-1[/tex]

[tex]\implies (3z-7)=0 \implies z=\dfrac{7}{3}[/tex]

To find the extraneous solution (the root that is not a root of the original equation), enter the two found values of z into the original equation:

[tex]\begin{aligned}z=-1\implies \sqrt{(-1)^2+8}&=1-2(-1)\\\implies 3&=3\implies \textsf{true}\\\end{aligned}[/tex]

[tex]\begin{aligned}z=\dfrac{7}{3} \implies \sqrt{\left(\frac{7}{3}\right)^2+8}&=1-2\left(\frac{7}{3}\right)\\\implies \dfrac{11}{3} &=-\dfrac{11}{3}\implies \textsf{false}\end{aligned}[/tex]

[tex]\textsf{As}\: \dfrac{11}{3} \neq -\dfrac{11}{3}\:\textsf{then}\: z=\dfrac{7}{3}\:\textsf{is the extraneous solution}[/tex]

Answer:

d.45 sq.ft

Step-by-step explanation:

Surface are i.e. Total surface area of square pyramid = a^2 + 2al

where a^2 is area of base

a is side of base

l is slant height

by the figure

a=3ft

a^2 = a×a

=3×3

=9ft

l=6ft

Surface area = a^2+2al

=9+2×3×6

=9+36

=45 sq.ft

Answer:

x = [tex]\frac{c-ab}{a}[/tex]

Step-by-step explanation:

a(x + b) = c ← distribute parenthesis on left side

ax + ab = c ( subtract ab from both sides )

ax = c - ab ( divide both sides by a )

x = [tex]\frac{c-ab}{a}[/tex]

Answer:

Just expand and solve for x :)

Answer:

L translated is now (6, -7)

Answer:

-1

-2

-5

-4

-1

Step-by-step explanation:

plug in each given number for x in the function:

- (-4) - 5

a negative negative is also a positive

4 - 5 = -1

- (-3) - 5

3 - 5 = -2

0 - 5 = -5

1 - 5 = -4

4 - 5 = -1

Answer:

n >= -1/4

Step-by-step explanation:

Divide both sides by the same factor, and flip the relation because the factor is negative

-28n/-28 >= 7/-28

Simplify,

Cancel terms that are in both the numerator and denominator.

n >= 7/-28

Divide the numbers.

n >= 7/-28 = n >= -1/4

The answer is n >= -1/4

Hope this helps!

Answer:

C) All squares are rhombuses. Rhombeses have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.

Step-by-step explanation: