Antoine made $33,284 last year. He receives a 4.5% annual raise. What will his new salary be

The number is -9

Step-by-step explanation:

Let x be the number then according to given statement

[tex]4x+10 = x-17[/tex]

Subtracting 10 from both sides

[tex]4x+10-10 = x-17-10\\4x = x-27[/tex]

Subtracting x from both sides

[tex]4x-x = x-x-27\\3x = -27[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3} = \frac{-27}{3}\\ x = -9[/tex]

Verification:

[tex]4(-9)+10 = -9-17\\-36+10=-26\\-26=-26[/tex]

The number is -9

Keywords: Linear equation, variables

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Slope formula: y2-y1/x2-x1

Line AB:

= 7-4/7-3

= 3/4

Line CD:

= 8-0/-6-0

= 8/-6

= -4\3

______

Best Regards,

Wolfyy :)

Step-by-step explanation:

speed= distance/time

time is meant to be in seconds

1mins = 60 secs

75mins =75 x 60 = 4500

distance is meant to be in metres

1metre= 0.001km

100 km = 100 x 1000= 100000

speed =distance/time

speed = 100000/4500

speed=22.22m/s

Answer:

[tex]\large\boxed{80\dfrac{km}{h}}[/tex]

Step-by-step explanation:

[tex]speed=\dfrac{distance}{times}\\\\\text{We have:}\\\\distance=100km,\ time=75min\\\\1h=60min\to1min=\dfrac{1}{60}h\\\\time=\dfrac{75}{60}h=\dfrac{5}{4}h=1.25h\\\\\text{Substitute:}\\\\speed=\dfrac{100km}{1.25h}=80\dfrac{km}{h}[/tex]

After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.

To find the height of the image after it has been scaled by 80% multiple times, we can use the formula for scaling:

[tex]\[ \text{New height} = \text{Original height} \times (\text{Scale factor})^{\text{Number of times scaled}} \][/tex]

Given that the original height is 150 mm and the scale factor is 80% (or 0.8), we can calculate:

a. After being scaled 3 times:

[tex]\[ \text{New height} = 150 \times (0.8)^3 = 150 \times 0.512 = 76.8 \, \text{mm} \][/tex]

b. After being scaled 6 times:

[tex]\[ \text{New height} = 150 \times (0.8)^6 = 150 \times 0.262 \approx 39.3 \, \text{mm} \][/tex]

As the image is scaled down by 80% each time, its height decreases significantly with each iteration.

After 3 times, it reduces to 76.8 mm, and after 6 times, it further reduces to approximately 39.3 mm.

These heights fall within the acceptable range for a U.S. passport photo (25-35 mm).

The probable question may be:

The distance from Elena's chin to the top of her head is 150 mm in an image. For a U.S. passport photo, this measurement needs to be between 25 mm and 35 mm. PASSPORT PHOTO 1. Find the height of the image after it has been scaled by 80% the following number of times. Explain or show your reasoning. a. 3 times b. 6 times

Answer: 15

Step-by-step explanation:

Recall : if sin α = cos β , then α + β are complementary , that is

α + β = 90

Since  sin (2x+7) = cos(4x-7) , then (2x+7) and (4x-7)  are complementary , that is:

2x + 7 + 4x - 7 = 90

6x = 90

x = 90/6

x = 15

The missing value x is constituting the angles of both sin and cos trigonometric ratios.

By using complementary property, the value of x for given condition is evaluated as 15.

The missing value x is constituting the angles of both sin and cos trigonometric ratios.

Its known by trigonometry that  when [tex]sin(\alpha) = cos(\beta)[/tex], then [tex]\alpha + \beta = 90^{\circ}[/tex]

Thus, we have:

[tex]2x + 7 + 4x - 7 = 90\\\\6x = 90\\\\x = \dfrac{90}{6}\\\\x = 15[/tex]

Thus, value of x for given condition is 15.

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Answer:

The length of the diagonal measures 54.2 meters

Step-by-step explanation:

Pythagorean theorem,

a² + b² = c²

a = 21

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

√2941 = c

54.23098... = c

54.2 = c

The length of the diagonal measures 54.2 meters.

We have given that,

A rectangular swimming pool is 21 meters

wide and 50 meters long.

We have to determine the length of the diagonal.

a² + b² = c²

a and b are sides of the triangle and c is the hypotenuse

a = 21,

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

Taking square root on both side

√2941 = c

54.23098 = c

54.2 = c

Therefore the length of the diagonal measures 54.2 meters.

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Answer:

C = 13%

Step-by-step explanation:

Answer:

The approximate perimeter of the trapezoid is 31 units

Step-by-step explanation:

step 1

Plot the trapezoid

Let

A(-5, -3), B(-2, 5), C(2, 5), and D(5, -3)

see the attached figure

step 2

Find the perimeter of trapezoid

we know that

The perimeter of trapezoid is equal to

[tex]P=AB+BC+CD+AD[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

we have

[tex]A(-5, -3),B(-2, 5)[/tex]

substitute in the formula

[tex]d=\sqrt{(5+3)^{2}+(-2+5)^{2}}[/tex]

[tex]d=\sqrt{(8)^{2}+(3)^{2}}[/tex]

[tex]d_A_B=\sqrt{73}\ units[/tex]

Find the distance BC

we have

[tex]B(-2, 5),C(2, 5)[/tex]

substitute in the formula

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

[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]

[tex]d_B_C=4\ units[/tex]

Find the distance CD

we have

[tex]C(2, 5),D(5, -3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-5)^{2}+(5-2)^{2}}[/tex]

[tex]d=\sqrt{(-8)^{2}+(3)^{2}}[/tex]

[tex]d_C_D=\sqrt{73}\ units[/tex]

Find the distance AD

we have

[tex]A(-5, -3),D(5, -3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3+3)^{2}+(5+5)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(10)^{2}}[/tex]

[tex]d_A_D=10\ units[/tex]

step 3

Find the perimeter

[tex]P=AB+BC+CD+AD[/tex]

substitute the values

[tex]P=\sqrt{73}+4+\sqrt{73}+10[/tex]

[tex]P=31\ units[/tex]

Answer:

[tex]\large\boxed{5\dfrac{1}{5}\ decimeters=52\ centimeters}[/tex]

Step-by-step explanation:

[tex]1\ dm=10\ cm\qquad\text{(1 decimeters = 10 centimeters)}\\\\\text{Therefore}\\\\5\dfrac{1}{5}\ dm=\dfrac{5\cdot5+1}{5}\ dm=\dfrac{26}{5}\ dm=\dfrac{26}{5}\cdot10\ cm=\dfrac{260}{5}\ cm=52\ cm[/tex]

To convert 5 1/5 decimeters to centimeters, you can multiply 5 by 10 and add the result to the centimeters part (1/5).

To convert decimeters to centimeters, we need to know that there are 10 centimeters in 1 decimeter. So, to convert 5 1/5 decimeters to centimeters, we can multiply 5 by 10 and add the result to the centimeters part (1/5). Converting 1/5 to centimeters gives us 2 centimeters. Therefore, 5 1/5 decimeters is equal to 51 centimeters.

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Answer:

D) 28+32

Step-by-step explanation:

4(7+8)=4(15)=60

Answer:

31 is a positive number, while -169, -369, and -569 is negative.

Step-by-step explanation:

Negative numbers, are numbers less then 0 and include a negative sign that looks like this "-".

Positive numbers are numbers above 0 and don't include a negative sign.

-169, -369, and -569 is negative because they have a negative symbol and the number is below 0, while 31 is positive because it's above 0 and doesn't include a negative sign.

Answer:

I think its 90°, since it l00ks like a right angle

Step-by-step explanation:

When a factor appears in both the numerator and denominator, that is a hole in the function.

Therefore, the domain of h(x) is (-∞, 4) (4, ∞).

Which means the range of h(x) is (-∞, 5) (5, ∞).

Graph: desmos.com/calculator/j58gdgugxy

Answer:

-4 = x

Explanation:

-11x +3x =-8x

24=-8x-8

+8= +8

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

32=-8x

--- -----

-8. -8

x= -4

To solve for x in the equation 24 =-11x-8+ 3x, combine like terms and isolate the variable by performing algebraic operations.

To solve for x in the equation 24 =-11x-8+ 3x, we can combine like terms:

Therefore, the solution for x is -4.

Distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.

Given that

Height of position of pilot from the ground = 30000 feet

Angle of depression when he looks down at runway = 6o

Need to measure along the ground, distance between runway and pilot that is horizontal distance between runway and pilot.

Consider the figure attached below

D represents position of runway.  

P represents position of pilot.

PG represents height of position of pilot from the ground that means PG = 30000 feet

PH is virtual horizontal line and HPD is angle of depression means ∠ HPD = 6 degree

AS DG and HP are horizontals, so DG is parallel to HP.

=>  ∠ HPD =∠ PDG =  6 degree  [ Alternate interior angle made by transversal PD of two parallel lines ]

We need to calculate DG

Consider right angles triangle PGD right angles at G

[tex]\text {As } \tan x=\frac{\text { Perpendicular }}{\text { Base }}[/tex]

[tex]\tan \angle \mathrm{PDG}=\frac{\mathrm{PG}}{\mathrm{GD}}[/tex]

[tex]\begin{array}{l}{=>\mathrm{GD}=\frac{\mathrm{PG}}{\tan \angle \mathrm{PDG}}} \\\\ {=>\mathrm{GD}=\frac{30000}{\tan 6^{\circ}}=285430.9336}\end{array}[/tex]

As one foot = 0.000189 miles

[tex]=>285430.9336 \text { feet }=285430.9336 \times 0.000189 \text { miles }=53.9464 \text { miles. }[/tex]

Hence distance between runway and pilot position along the ground is 285430.9336 feet that is 53.9464 miles.

Final answer:

To find the distance to the runway, we can use trigonometry and create a right triangle using the pilot's height and the angle of depression. Using the tangent function, we can solve for the distance. The pilot is approximately 58.47 miles away from the runway.

Explanation:

To find the distance to the runway, we can use trigonometry. The angle of depression of 6 degrees tells us that the runway is below the pilot's line of sight. We can create a right triangle with the pilot's height of 30,000 feet as the opposite side and the distance to the runway as the adjacent side. Using the tangent function, we can solve for the distance:

Tan(6) = Opposite/Adjacent

Tan(6) = 30,000/Adjacent

Adjacent = 30,000/Tan(6)

Using a calculator, we find that the pilot is approximately 308,517 feet away from the runway.

To convert this distance to miles, we divide by 5,280 (since there are 5,280 feet in a mile):

308,517/5,280 ≈ 58.47 miles

Therefore, the pilot is approximately 58.47 miles away from the runway.

Answer: No, he burns 480

Step-by-step explanation: you multiply 8 by 60, the amount of minutes in an hour

See the explanation

Since you haven't provided any options I'll face this problem in a general way. Linear functions are given of the form:

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

This is called the slope-intercept form of the equation of a line. When modeling a linear function we need to take into account that we will have a constant rate of change and that when plotting our model this will follow a line. In order to model a problem as a linear function we need to follow some tips:

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The quantity that is best modeled by a linear function must fit into y = mx + c

A model is a representation of reality. There are many different types of models such as;

A linear function is a function of the sort y =mx + c. The quantity is not shown in the question hence the question is incomplete.

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Answer:

[tex]1\dfrac{1}{4}a^6b^3[/tex]

Step-by-step explanation:

A square of a monomial is [tex]1\dfrac{9}{16}a^{12}b^6[/tex] that is [tex]\dfrac{25}{16}a^{12}b^{6}[/tex]

Use properties of exponents:

[tex](a^m)^n=a^{mn}\\ \\\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m\\ \\a^mb^m=(ab)^m[/tex]

Note that

[tex]\dfrac{25}{16}=\dfrac{5^2}{4^2}=\left(\dfrac{5}{4}\right)^2\\ \\a^{12}=a^{6\cdot 2}=(a^6)^2\\ \\b^6=b^{3\cdot 2}=(b^3)^2[/tex]

Then

[tex]\dfrac{25}{16}a^{12}b^{6}=\left(\dfrac{5}{4}\right)^2\cdot (a^6)^2\cdot (b^{3})^2=\left(\dfrac{5}{4}a^6b^3\right)^2[/tex]

So, the monomial is

[tex]\dfrac{5}{4}a^6b^3=1\dfrac{1}{4}a^6b^3[/tex]

Answer:

The rate of interest applied fro compound interest is 24.5 %  

The rate of interest applied simple interest is 37.5 %

Step-by-step explanation:

Given as :

The Principal amount that is deposited = $ 800

The Time period = 24 months = 2 years

The Interest earn = $ 200

Let the rate of interest = R %

So, The Amount = Principal deposited - interest earn

Or, A = $ 800 - $ 200

∴ Amount = $ 600

From compounded method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]

Or, $ 600 = $ 200 × [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]

Or, [tex]\frac{600}{200}[/tex] = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]

Or, 3 = [tex](1+\dfrac{\textrm R}{100})^{\textrm 2}[/tex]

Or, [tex]3^{\frac{1}{2}}[/tex] = (1 +[tex]\frac{R}{100}[/tex])

Or, 1.245 = (1 +[tex]\frac{R}{100}[/tex])

or, 1.245 - 1 = [tex]\dfrac{R}{100}[/tex]

or, 0.245 × 100 = R

So, the rate is = 24.5 %

Hence The rate of interest applied fro compound interest is 24.5 %  Answer

From Simple Interest method

Simple Interest = [tex]\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}[/tex]

Or, $ 600 = [tex]\dfrac{\textrm 800\times \textrm R\times \textrm 2}{100}[/tex]

Or,  $ 600 × 100 = $ 800 × R × 2

Or, R = [tex]\frac{60000}{1600}[/tex]

∴ R = 37.5 %

So, The rate is 37.5 %

Hence The rate of interest applied simple interest is 37.5 %Answer

Answer:

7-c < 30

Step-by-step explanation:

its in your question.

Answer: 12

Step-by-step explanation: To solve this equation, since x is being divided by 2, in order to get x by itself, we need to multiply by 2 on both sides of the equation.

On the left side of the equation, the 2's cancel and we have x and on the right side of the equation, 6 × 2 gives us 12 so we have x = 12 which is the solution for our equation.

To check our solution, we plug 12 in for x in the original equation.

Image provided.

Answer:

Speed of Carol is 78 mph and that of Steve is 84 mph.

Step-by-step explanation:

Let the speed of Carol is x mph and that of Steve is (x + 6) mph.

If they move towards each other with that speed, then the resultant speed will be (x + x + 6) = (2x + 6) mph

With this resultant speed, they cover 405 miles in 2.5 hours.

So, [tex]2x + 6 = \frac{405}{2.5} = 162[/tex]

⇒ 2x = 156

⇒ x = 78 mph

So, speed of Carol is 78 mph and that of Steve is (78 + 6) = 84 mph. (Answer)

For this case we must solve the following equation:

[tex]\frac {x} {4} + 2 = -12[/tex]

Subtracting 2 from both sides of the equation we have:

[tex]\frac {x} {4} = - 12-2[/tex]

Equal signs are added and the same sign is placed.

[tex]\frac {x} {4} = - 14[/tex]

Multiplying by 4 on both sides of the equation we have:

[tex]x = -14 * 4\\x = -56[/tex]

Thus, the solution of the equation is [tex]x = -56[/tex]

Answer:

[tex]x = -56[/tex]

√5 • √80

Combine the two using the product rule for radicals:

√(5 • 80)

Multiply:

√400

Rewrite 400 as 20^2

√20^2

= 20

The answer is 20

Answer:

Step-by-step explanation:

-8(k - 4)         use the distributive property: a(b + c) = ab + ac

= (-8)(k) + (-8)(-4) = -8k + 32

Answer:

-8k+32

Step-by-step explanation:

-8(k-4)=-8k+32

Answer:

D) 0.0004

Step-by-step explanation:

(0.02)^2=0.02*0.02=0.0004

Answer:

a. yes

b. no

c. yes

d. yes

Step-by-step explanation:

For a, 27 + 38 can be broken apart. 27 is broken up by adding smaller numbers (20 + 7 = 27) and the same is done with 38 (30 + 8 = 38), so A and C shows a way to add 27 and 38. In C, the numbers are just put into a different order. B is not a way to add 27 and 38, because the sum is different.

27 + 38 = 65, however 20 + 70 + 38 = 128. The addition problem for D is a way to solve for 27 + 38, because it is broken up differently than A and C. They instead added the 20 and 30 together first, then split up 15 (from 8+7) into 10 and 5. So D is a way to solve, because it gets the same answer as 27 and 38 :D

Answer:whole wheat

Step-by-step explanation:

Its whole wheat because when you divide the cost by the weight whole wheat is the best deal

Answer:

14,747.20

There are 52 weeks in a year being paid bi-weekly means being paid every other week or 26 times a year. So 567.20 * 26 is 14747.20.

Answer:

6

Step-by-step explanation:

it's asking how much makes 10% of 60 and to find it we use this formula :

60 ÷ 100 × 10 = 6

Answer:

6 milkshakes

Step-by-step explanation:

All you need to do is multiply:

60 (0.10) = 6