Find the measure of angle 2.

30°

120°

60°

ANSWER

[tex]y \leqslant - x + 4[/tex]

EXPLANATION

The equation of the boundary line is

[tex]y = - x + 4[/tex]

Hence the inequality is either

[tex]y \leqslant - x + 4[/tex]

or

[tex]y \geqslant - x + 4[/tex]

We test the origin to get determine which one represents the shaded

We substitute (0,0) into the first inequality to get;

[tex]0\leqslant - (0) + 4[/tex]

This implies that,

[tex]0 \leqslant 4[/tex]

Hence the correct answer is

[tex]y \leqslant - x + 4[/tex]

Answer: Second Option

[tex]y \leq -x +4[/tex]

Step-by-step explanation:

The region is bounded by a line of negative slope that cuts the y-axis at the point y = 4 and cuts the x-axis at the point x = 4.

So the equation of this line is

[tex]y = -x + 4[/tex]

If the region is composed of all the points that lie below the line y = -x + 4 then it means that the region is formed by all the values of y less than or equal to the line [tex]-x + 4[/tex].

Therefore the inequation is:

[tex]y \leq -x +4[/tex]

Second Option

Answer:

26

Step-by-step explanation:

Area of a triangle is:

A = 1/2 b h

Given b = 13 and h = 4:

A = 1/2 (13 cm) (4 cm)

A = 26 cm²

Answer:

A

Step-by-step explanation:

Given

-4x²(5[tex]x^{4}[/tex] - 3x² + x - 2)

Multiply each term in the parenthesis by - 4x²

= - 20[tex]x^{6}[/tex] + 12[tex]x^{4}[/tex] - 4x³ + 8x²

Answer:

A

Step-by-step explanation:

Answer:

25. The area of the trapezoid is 96 cm² ⇒ 2nd answer

26. The area of the kite is 40.8 feet² ⇒ 3rd answer

31. The area of the circle is 6.0025π m² ⇒ 3rd answer

Step-by-step explanation:

* Lets solve the problems

25. The figure is trapezoid

- The trapezoid has two parallel bases base 1 and base 2

- The area of the trapezoid is 1/2(base 1 + base 2) × height

- The length of base 1 is 12 cm

- The length of its height is 6 cm

- The length of the base 2 is (2 + 12 + the adjacent side to ∠45°)

- To find the missing part in the base 2 use the trigonometry

  function tan 45° = opposite/adjacent

∵ tan 45° = opposite/adjacent

∵ The opposite = 6

∵ tan 45° = 1

∴ 1 = 6/adjacent ⇒ by using cross multiplication

∴ The adjacent = 6 cm

∴ The length of base 2 = 2 + 12 + 6 = 20 cm

∵ The area of the trapezoid is 1/2(base 1 + base 2) × height

∵ The length of base 1 = 12 cm

∵ The length of base 2 = 20 cm

∵ The length of its height = 6 cm

∴ The area = 1/2(12 + 20) × 6 = 1/2(32) × 6 = 16 × 6 = 96 cm²

* The area of the trapezoid is 96 cm²

26. The figure is kite

- The kite has two diagonals

- Its diagonals perpendicular to each other

- The longest diagonal bisects the shortest diagonal

- The area of the kite is 1/2(diagonal 1 × diagonal 2)

∵ The length of diagonal 1 = 10.2 feet

∵ The length of diagonal 2 = 8 feet

∵ The area of the kite = 1/2(diagonal 1 × diagonal 2)

∴ The area = 1/2(10.2 × 8) = 1/2(81.6) = 40.8 feet²

* The area of the kite is 40.8 feet²

31. The figure is a circle

- The circle has diameter

- The radius is half the diameter

- The area of the circle is π r²

∵ The length of the diameter = 4.9 m

∵ The length of the radius 1/2 the length of the diameter

∴ The length of the radius = 1/2 (4.9) = 2.45 m

∵ The area of the circle = π r²

∴ The area = π (2.45)² = 6.0025π m²

* The area of the circle is 6.0025π m²

Answer:

25) 96 cm²

26)  40.8 ft ²

31).  6.0025π m²

Step-by-step explanation:

25) To find the area of trapezoid

Area of trapezoid = h(a + b)/2

Here a = 6 + 12 + 2 = 20 cm

b = 12 cm and h = 6

Area =  h(a + b)/2

 = 6(20 + 12)/2

 = 96 cm²

26) To find the area of kite

Area of kite = pq/2

Where p and q are the two diagonals

Here p = 10.2 ft and q = 8 ft

Area = pq/2

 = (10.2 * 8)/2 = 40.8 ft²

31) To find the area of circle

Area of circle = πr²

Here r = 4.9/2 = 2.45 m

Area = πr²    

 = π *(2.45)²

 = 6.0025π m²

Answer: Third option.

Step-by-step explanation:

These are some transformations for a function f(x):

If [tex]f(x)-k[/tex], then the function is shifted down "k" units.

 If [tex]f(x-k)[/tex], then the function is shifted right "k" units.

Knowing this we can describe the transformation from the graph of the function [tex]f(x) = x^2[/tex] to the graph of the function [tex]f(x) = (x - 3)^2-1[/tex]. This is:

The function  [tex]f(x) = (x - 3)^2-1[/tex] is the function [tex]f(x) = x^2[/tex] but shifted right 3 units and shifted down 1 units.

Therefore, the correct option is the third one.

Answer:

right 3 units, down 1 unit

Answer:

no solutions

Step-by-step explanation:

4x + 2y = –14

6x + 3y = –22

Divide the first equation by 2 and the second equation by 3

4x/2 + 2y/2 = –14/2     2x +y = -7

6x/3 + 3y/3 = –22/3    2x + y = -22/3

The left hand sides are the same but the right hand sides are different.

Multiply the second equation by -1

2x+y = -7

-2x -y = 22/3

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

0 = -7+22/3

0 = 1/3

This is never true, so there are no solutions

Answer:

B, No Solutions

Step-by-step explanation:

Answer:

   √6 + √2

= --------------

        4

Step-by-step explanation:

15° = 45° - 30°

So

cos(15)  = cos(45 - 30)

=cos(45)  × cos(30) + sin(45) × sin(30)

= 1/√2  × (√3)/2  + 1/√2 × 1/2

    (√3) + 1

= --------------

     2√2

    (√3) + 1              √2

= -------------- x       ---------

     2√2                  √2

   √6 + √2

= --------------

        4

Answer:

see explanation

Step-by-step explanation:

Using the addition formula for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

and exact values

sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex]

c0s30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex]

Express cos15° = cos(45 - 30 )°, then

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] + ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )

= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]

= [tex]\frac{\sqrt{6}+\sqrt{2}  }{4}[/tex] ← exact value

Answer:

Part 1) [tex]z=4\sqrt{2}\ units[/tex]

Part 2) [tex]x=18\ units[/tex]

Part 3) [tex]y=12\sqrt{2}\ units[/tex]

Step-by-step explanation:

step 1

Find the value of z

In the smaller right triangle IFG of the figure

Applying the Pythagoras Theorem

[tex]6^{2}=2^{2}+z^{2}[/tex]

[tex]z^{2}=6^{2}-2^{2}[/tex]

[tex]z^{2}=32[/tex]  

[tex]z=4\sqrt{2}\ units[/tex]

step 2

In the right triangle HFG

Applying the Pythagoras Theorem

[tex]x^{2}=y^{2}+6^{2}[/tex]

[tex]y^{2}=x^{2}-36[/tex] -----> equation A

step 3

In the right triangle HIG

Applying the Pythagoras Theorem

[tex]y^{2}=z^{2}+(x-2)^{2}[/tex]

[tex]y^{2}=32+(x-2)^{2}[/tex] -----> equation B

step 4

equate equation A and equation B

[tex]x^{2}-36=32+(x-2)^{2}\\x^{2}-36=32+x^{2}-4x+4\\4x=36+36\\4x=72\\x=18\ units[/tex]

step 5

Find the value of y

Substitute the value of x in the equation B

we have

[tex]x=18\ units[/tex]

[tex]y^{2}=32+(18-2)^{2}[/tex]

[tex]y^{2}=32+(16)^{2}[/tex]

[tex]y^{2}=288[/tex]

[tex]y=12\sqrt{2}\ units[/tex]

Answer:

216

Step-by-step explanation:

Anything to the zero power is equal to 0.

The denominator can be moved to the numerator because the exponent is negative. So it is now 1*6^3. This is equal to 216.

The value of expression [tex]\frac{d^{0} }{w^{-3} }[/tex] is 216

The correct option is (B).

Power can be defined as an expression that represents repeated multiplication of the same number whereas exponent is the quantity that represents the power to which the number is raised.

Given:

[tex]\frac{d^{0} }{w^{-3} }[/tex]

put d=-5 and w=6

So, [tex]\frac{-5^{0} }{6^{-3} }[/tex]

=1/[tex]6^{-3}[/tex]   [a°=1]

=6³      [[tex]1/a^{-b} = a^{b}[/tex]]

=216.

hence,  [tex]\frac{d^{0} }{w^{-3} }[/tex] = 216.

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Answer:

(x-3)^2 + (y-1)^2 = 4

Step-by-step explanation:

The equation of a circle is usually written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

The center is at the origin so (h,k) = (3,1) and  the radius is 2 so r=2

(x-3)^2 + (y-1)^2 = 2^2

(x-3)^2 + (y-1)^2 = 4

For this case, we convert the mixed numbers to fractions:

Box 1: [tex]4 \frac {2} {3} = \frac {3 * 4 + 2} {3} = \frac {14} {3}[/tex]

Box 2: [tex]5 \frac {3} {8} = \frac {8 * 5 + 3} {8} = \frac {43} {8}[/tex]

We add the fractions to find the total weight of the boxes:

[tex]\frac {14} {3} + \frac {43} {8} = \frac {8 * 14 + 43 * 4} {3 * 8} = \frac {112 + 172} {24} = \frac {284 } {24} = \frac {142} {12} = \frac {71} {6}[/tex]

Thus, between the two boxes weigh[tex]\frac {71} {6}[/tex] ounces.

In mixed number: [tex]11 \frac {5} {6}[/tex]

Answer:

[tex]11 \frac {5} {6}[/tex]ounces

The total weight of the two boxes is 10 1/24 ounces, found by converting the mixed numbers into improper fractions, finding a common denominator, and adding the fractions together.

To find the total weight of two boxes when one weighs 4 2/3 ounces and the other weighs 5 3/8 ounces, we first convert the mixed numbers into improper fractions. For 4 2/3 ounces, this would be (4 × 3) + 2 = 14/3 ounces. For 5 3/8 ounces, it is (5 × 8) + 3 = 43/8 ounces. Once in improper fraction form, we find a common denominator, which is 24, and then we add the two fractions together.

The first box in twenty-fourths is (14/3) × (8/8) = 112/24. The second box is (43/8) × (3/3) = 129/24. Adding them gives us 112/24 + 129/24 = 241/24. We divide 241 by 24, which results in 10 with a remainder of 1, giving us 10 1/24 ounces.

Therefore, the total weight of the two boxes is 10 1/24 ounces.

[tex]\bf Px+35=-6x+Q\implies \stackrel{P}{~~\begin{matrix} -6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}x+35=~~\begin{matrix} -6x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+\stackrel{Q}{35}\implies 35=35[/tex]

whenever you get an equality like so, that's a flat that both equations are exactly one and the same and thus the system has "infinitely many solutions".

Answer:

79°

Step-by-step explanation:

given both figures are congruent, and one is simply a rotation of another

m∠B corresponds to m∠k = 79°

Answer:

Given that DMKT → FCBN, B is 79°

Step-by-step explanation:

m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N

m∠K = 79° therefore m∠B = 79°.

Please mark brainliest and have a great day!

Answer:

4 miles

Step-by-step explanation:

6 divided by 3 = 2 = one-third of 6

--> multiply by two to get two thirds of six = 4 miles

Answer:

4 miles

Step-by-step explanation:

Answer:

See below in BOLD.

Step-by-step explanation:

y = -3x 2 + 18x - 2

y = -3(x^2 - 6x) - 2

y = -3 [ (x - 3)^2 - 9] - 2

y = -3(x - 3)^2  + 25  is vertex form.

The  coefficient of x^2 is negative so we have a maximum  value of the function.

The maximum value is 25 and the axis of symmetry is x = 3.

Answer: The maximum value is 25 and the axis of symmetry is x = 3.

Answer:

The correct answer is [tex]9x^{2}-6x[/tex].

Step-by-step explanation:

Consider the provided division:

We need to perform the subtraction in the division:

[tex]6x^{3}+x^{2}-10x[/tex]  ......(1)

[tex]6x^{3}-8x^{2}-4x[/tex]  ......(2)

In order to perform the subtraction simply change the sign of the second expression.

  [tex]6x^{3}+x^{2}-10x[/tex]

[tex]-6x^{3}+8x^{2}+4x[/tex]

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

           [tex]9x^{2}-6x[/tex]

Therefore, the correct answer is [tex]9x^{2}-6x[/tex].

Answer:

Step-by-step explanation:

Answer:C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

Step-by-step explanation:

The margin of error implies that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

Given that the organization polled a random sample of its employees regarding their new vacation policy.

Now, 83% of the workers polled assessed the vacation policy as "delightful," with a margin of error of ±2% and a confidence interval of 95%, implying that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

Hence, the margin of error implies that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

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Answer:

Answer: f[c(p)] = 0.9265p

Step-by-step explanation:

Given: Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is , where p is the original price of the car.

He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is , where c is the sale price of the car.

Now, the composite function that can be used to calculate the final price of Jonah's car is given by :-

Answer:

f[c(p)] = 0.9265p

Step-by-step explanation:

c(p) = 0.85p

f(c) = 1.09c

f[c(p)] = f[0.85p] = 1.09(0.85p) = 0.9265p

Answer: f[c(p)] = 0.9265p

Answer:

it's d or the fourth option

Step-by-step explanation:

Answer:

y=x-5

Step-by-step explanation:

"output" means  y

and "input" means  x

So all you need to find is the =

Please mark brainliest and have a great day!

[tex]\bf (2x^2-3x)^2+4(2x^2-3x)+3=0\qquad \boxed{a=2x^2-3x}\implies a^2+4a+3=0 \\\\\\ (a+3)(a+1)=0\implies a= \begin{cases} -3\\ -1 \end{cases}\qquad \stackrel{\textit{their sum}}{-3-1\implies -4}[/tex]

Answer:

3/2

Step-by-step explanation:

(2x² − 3x)² + 4 (2x² − 3x) + 3 = 0

We can simplify this using substitution.  Let's say that u = 2x² − 3x.

u² + 4u + 3 = 0

Factoring:

(u + 3)(u + 1) = 0

u = -3, u = -1

Therefore:

2x² − 3x = -3, 2x² − 3x = -1

2x² − 3x + 3 = 0, 2x² − 3x + 1 = 0

For a quadratic ax² + bx + c = 0, the sum of the roots is -b/a.  So in both cases, the sum is 3/2.

Answer:

12.75

Step-by-step explanation:

John picked out 12.75 apples on the big tree.

15% of 85 is 12.75.

Hope this helps! Please mark brainliest!

Answer:

approx 13 apples

Step-by-step explanation:

total apples : 85

given john picked 15% = 0.15 of the total apples

number of apples john picked = 0.15 x 85 = 12.75

rounding off to nearest whole number (because you can't really pick 0.75 of an apple) = 13 apples

Answer:

Two solutions

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

Both lines have a slope m = - [tex]\frac{1}{2}[/tex]

Hence the lines are parallel and have no points of intersection

Thus the system has no solution → A

Answer:

Δy = 15

Step-by-step explanation:

Δy represents the change in the y-coordinates

We are given points (-3,-5) and (0,10)

here y₁ = -5 and y₂ = 10

so, delta y will be

Δy = y₂ - y₁

Δy = 10 -(-5)

Δy = 10 + 5

Δy = 15

So, delta y Δy =15

[tex]\bf \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 2\ln(3)=\ln(x-4)\implies \ln(3^2)=\ln(x-4)\implies \ln(9)=\ln(x-4) \\\\\\ \log_e(9)=\log_e(x-4)\implies e^{\log_e(9)}=e^{\log_e(x-4)}\implies 9=x-4\implies \boxed{13=x}[/tex]

Answer:

11 animals

Explanation:

-Sparkles is the first animal that is introduced, then the monkey is the second. Since there are 18 eyes, that can be divided by 2 to tell you how many of the remaining animals there are. Which would lead up to 9 and 9+2=11

Eleven (11) Animals

Based on the above given information, it can be construed that that Eleven (11) animals are in the forest.

The first mentioned animal is Sparkles the Unicorn (Animal 1) who probably might be hungry and, might have searched through the forest to get the nice big juicy apple.

She might have dodged several wild predating animals just for luck to smile on her through the discovery of a big juice apple. She plucks it, and starts eating. A nearby lurking, cunning monkey (Animal 2), snatches the fruit from Sparkles the Unicorn, due to her carelessness, and as she proceed to retrieve the fruit, she discovered that that wasn’t the only monkey around. She sees eighteen (18) pairs of eyes which means, there are nine (9) other animals i.e. 18 pairs of eyes divided by 2 (18/2 = 9) are also in the forest.

Therefore:

Animal 1 + Animal 2 + 9 other Animals = 11 Animals

This kind of question can be said to be a Mathematical Puzzle.

Mathematical puzzle is a form of recreational mathematics, which helps to enhance students’ knowledge.

Mathematical puzzle helps students to understand different concepts of mathematical problems.

This form of mathematical improve students’ learning ability

KEYWORDS:

Answer:

d = 7.5t

Step-by-step explanation:

t = time

d= distance

you want to write an equation that compares time with distance.

in the question it says per hour whoch means 7.5 miles have been ran each hour. however we dont know how mmany hour lets say tom has ran. therefore, we use t instead. we got d to go behind the = sign because we are comparing. When we multiply 7.5t we are going to get the distance he ran, d.

hope this helps!

Answer:

d=7.5t

Step-by-step explanation:

Answer:

14 cm

Step-by-step explanation:

step 1

Find the actual length of the segment

we know that

The original scale is 1 cm : 4m

In the original drawing, the length of a segment is 7 cm

therefore

Let

x ----> the actual length of the segment

by proportion

1/4=7/x

x=4*7

x=28 m

step 2

Find the length of the segment in the new drawing

The new scale is 1cm : 2m

Let

x ---> the length of the segment in the new drawing

by proportion

Remember that

The actual length is 28 m

1/2=x/28

x=28/2

x=14 cm