Does anyone know how to solve this? A motorist and a bicyclist leave the same place and proceed in opposite directions. If the bicycle is traveling 15 mph and the auto is traveling 55 mph, in how many hours will they be 140 miles apart?

Answer:

missing value b is 14

Step-by-step explanation:

We have been given the modulus of a complex number which is

[tex]r=\sqrt{a^2+b^2}[/tex]

Here on comparing the given complex number with general a+bi we get:

a=48 and b=b

On substituting the values in the formula for modulus we get:

[tex]\sqrt{48^2+b^2}=50[/tex]

[tex]\Rightarrow 2304+b^2=50^2[/tex]

[tex]\Rightarrow b^2=2500-2304[/tex]

[tex]\Rightarrow b^2=196[/tex]

[tex]\Rightarrow b=\sqrt{196}[/tex]

[tex]\Rightarrow b=14[/tex]

Therefore, missing value b is 14

Answer: 14

Step-by-step explanation:

Edg 2021

Answer:

kora is 13

Step-by-step explanation:

venla is 5 years older than kora

18-5=13

Answer: The Equation answer is V=k+5

how old is kora when venla is 18 years old? Is 13 years old

Step-by-step explanation:

Answer:

B L is equal to P minus 2W all over 2

Step-by-step explanation:

P = 2L + 2W

We want to isolate L.

The first step is to subtract 2W from each side.

P-2W = 2L + 2W-2W

P-2W = 2L

Now divide each side by 2

(P-2W)/2 = 2L/2

(P-2W)/2 = L

Answer:

49

Step-by-step explanation:

If so  the inter quartile range = 58 - 9 = 49

Answer:

the answer would be 49 i hope this helps

Step-by-step explanation:

Answer:

Fir trees are 9 meters and the pine trees are 12 meters tall.

Step-by-step explanation:

Let the height of the fir tree = x and the height of the pine tree = y (in meters).

It is given that the combined height of both the trees is 21 meters.

That is, [tex]x+y=21[/tex]

Also, the height of 4 fir trees is 24 meters more than that of the pine tree.

That is, [tex]4x=y+24[/tex] i.e. [tex]4x-y=24[/tex]

So, we get the system of equations,

x+y=21

4x-y=24

Adding both the equations, gives us,

5x = 45 i.e. x=  9.

So, x+y=21 ⇒ y= 21 - x ⇒ y= 21 - 9 ⇒ y= 12.

Thus, the fir trees are 9 meters tall and the pine trees are 12 meters tall.

Answer:

BE =40

Step-by-step explanation:

Since this is a regular pentagon

BE = BD

3x+4 = 2x+16

Subtract 2x from each side

3x-2x +4 = 2x-2x+16

x+4 = 16

Subtract 4 from each side

x+4-4 = 16-4

x =12

We want to know the length of BE

BE = 3x+4

x=12 so we can substitute it in

      3(12) +4

       36+4

    40

BE =40

Answer:

Option D) Angle D is not an exterior angle.

Step-by-step explanation:

An exterior angle of a triangle is formed between the extended line DF and line DE.

This means Exterior angle of a triangle is supplementary to the interior angle formed on the same line.

So, exterior angle D + ∠ EDF should be equal to  180° [ By definition ]

Therefore, angle D shown in the diagram is not the exterior angle.

Option D is the answer.

Answer: 93

Step-by-step explanation:

NOTE: "won" means add, "spent" means subtract

Monday: + 75

Tuesday: Monday + 105   = 75 + 105   = 180

Wednesday: Tuesday + 127 - 250   =   180 + 127 - 250   = 57

Jared has 57 but needs 150

(75+105)+127= 307

307-250=57

jared has 57 tickets he wants to 150 ticket prize

57-150=93

Jared needs 93 tickets to get the prize

To represent the remaining weight that can be added to the elevator, write and solve the inequality 800 - 95 ≥ x. The remaining weight is 705 pounds or less.

To represent the remaining weight that can be added to the elevator, we can use an inequality. Let's assume that the remaining weight is represented by 'x' pounds. The total weight the elevator can carry is 800 pounds. So, the inequality can be written as:

800 - 95 ≥ x

To solve the inequality, we subtract 95 from both sides:

x ≤ 800 - 95

x ≤ 705

Therefore, the remaining weight that can be added to the elevator is 705 pounds or less.

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Answer:

1 1/2 hours

Step-by-step explanation:I took the test

Answer:

  D.  y = 4/5x

Step-by-step explanation:

Equations A and C are not in slope-intercept form.

Equation B has a y-intercept of -5, which the graph does not.

The only viable choice is D.

Answer:

the answer is 55

Step-by-step explanation:

all angles have to  equal up to 180.

55+30=85

85+40=125

180-125=55

Answer:

$1500 is a reasonable estimate.

Exact total cost of the clothing is $1536.

Step-by-step explanation:

We have been given that a clothing sells 26 shirts and 22 pairs of jeans. Each item of clothing costs $32.

First of all, we will find the estimate of price of clothing by rounding to nearest tens as:

[tex]26\approx 30[/tex]

[tex]22\approx 20[/tex]

[tex]\$32\approx \$30[/tex]

Estimated number of clothing would be [tex]30+20=50[/tex]

Estimated cost would be [tex]\$30\times 50=\$1500[/tex]

Therefore, $1500 is a reasonable estimate for the total cost of the clothing.

Let us find exact total number of clothing by adding 26 and 22 as:

[tex]26+22=48[/tex]

Exact total cost of clothing would be [tex]\$32\times 48=\$1536[/tex]

Therefore, the exact total cost of the clothing is $1536.

The equation of the line that passes through the given points is 3y + 4x = -3

From the question,

We are to determine the equation of the line that passes through the points (-3,3) and (9,-13)

The equation can be determined by using the formula for calculating the equation of a line with two given points.

The formula for determining the equation of a straight line with two given points (x₁, y₁) and (x₂, y₂) is

[tex]\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

From the question,

x₁ = -3

y₁ = 3

x₂ = 9

y₂ = -13

Putting the parameters into the formula, we get

[tex]\frac{y-3}{x--3}= \frac{-13-3}{9--3}[/tex]

This becomes

[tex]\frac{y-3}{x+3} = \frac{-16}{12}\\[/tex]

Then,

[tex]\frac{y-3}{x+3}=\frac{-4}{3}[/tex]

This becomes

[tex]3(y-3) = -4(x+3)[/tex]

Clearing the brackets, we get

[tex]3y -9 = -4x -12[/tex]

[tex]3y+4x= -12 +9[/tex]

[tex]3y +4x =-3[/tex]

Hence, the equation of the line that passes through the given points is 3y + 4x = -3

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The linear equation that passes through the points (-3,3) and (9,-13) can be found by first calculating the slope (m) using the formula (y2 - y1) / (x2 - x1), giving m = -4/3. Next, substitute one of the points and the slope into the slope-intercept form of a linear equation, y = mx + b, to solve for the y-intercept (b), resulting in b = -1. Thus, the desired linear equation is y = -4/3x - 1.

To write a linear equation that passes through two points (-3,3) and (9,-13), we first need to find the slope (m) of the line. The formula to find the slope is (y2 - y1) / (x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Therefore, m = (-13 - 3) / (9 - (-3)) = -16/12 = -4/3.

Next, we use the slope-intercept form of a linear equation, y = mx + b where 'm' is the slope, and 'b' is the y-intercept. We can substitute one of our points and the slope into this equation to solve for b. Let's use the point (-3,3). So, 3 = (-4/3)*(-3) + b. This simplifies to 3 = 4 + b. Solving for b gives b = 3 -4 = -1.

Therefore, the linear equation that passes through the points (-3,3) and (9,-13) is y = -4/3x - 1.

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Answer:

D = 130

Step-by-step explanation:

We can use the formula

<Y = 1/2 (big arc XZ - little arc XZ)

50 = 1/2 ( 230- XZ)

Multiply by 2 on each side

100 = 230-XZ

Subtract 230 from each side

100-230 = 230-230 -XZ

-130 = -XZ

Multiply each side by -1

-1*-130 = -1 * -XZ

130 = XZ

Answer:

D. the measure of xz is 130 degrees

Step-by-step explanation:

The correct answer is 130 degrees

Answer:

The GCF of 35 and 39 is 1.

Step-by-step explanation:

Factors of 35: 1, 5 and 7

Factors of 39: 1, 3, 13

1 is the only factor that these numbers have in common.

Hope this helps!

Answer:

35 - 1, 5, 7

39 - 1, 3, 13

the greatest common factor will be 1

hope this helps

Step-by-step explanation:

Answer:

35%

Step-by-step explanation:

So we can write that 14/40 of the group is allergic to peanuts. So 7/20 of the group are allergic or 35/100.

Answer:

since the lines don't intersect there is no solution.

Look at the picture.

[tex]A_1=15\cdot6=90\ cm^2\\\\A_2=5\cdot5=25\ cm^2\\\\A_3=5\cdot4=20\ cm^2\\\\A_4=6\cdot8=48\ cm^2\\\\A_5=15\cdot2=30\ cm^2\\\\A_6=2\cdot2=4\ cm^2\\\\A_7=15\cdot8=120\ cm^2\\\\A_8=15\cdot6=90\ cm^2\\\\S.A.=A_1+2A_2+5A_3+2A_4+2A_5+2A_6+A_7+A_8\\\\S.A.=90+2\cdot25+5\cdot20+2\cdot48+2\cdot30+2\cdot4+120+90\\\\\boxed{S.A.=614}\ cm^2[/tex]

Eff started his lemonade stand with $22 and ended the day with $110, having earned five times his starting amount.

Eff started his day with a certain amount of money and ended up with $110 at the end of the day after earning five times the amount he started with. To calculate the amount Eff started with, we need to set up a simple equation based on the given information. Let x represent the amount of money Eff had at the beginning of the day. The relationship can be expressed as:

5x = $110

Divide both sides of the equation by 5 to find the starting amount:

x = $110 / 5

x = $22

Therefore, Eff started the day with $22.

Answer:

period

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Final answer:

The expression 12/a + 2a - 8 is not a polynomial because it contains a variable in the denominator, thus violating the definition of polynomials that only allow non-negative integer exponents.

Explanation:

The expression 12/a + 2a - 8 is best described as an option (d), not a polynomial because it contains a term with a variable in the denominator (12/a). Polynomials are algebraic expressions that consist only of non-negative integer powers of the variable. In this case, the term 12/a has a variable 'a' in the denominator, which implies a negative exponent if it were to be written with only the variable in the numerator. This is why the expression does not fit the definition of a polynomial.

Answer:

hello :

the graph passes by ( 3; -1/3)  : f(3) = -1/3

a/ (3)^3 = -1/3

a / 27 = -1/3

a/9 = - 1

a = - 9

We have the point:

[tex]\left(3,\ -\dfrac{1}{3}\right)[/tex]

Put the coordinates of the point to the equation of the function f:

[tex]f(x)=\dfrac{a}{x^3}\to y=\dfrac{a}{x^3}\\\\\left(3,\ -\dfrac{1}{3}\right)\to x=3,\ y=-\dfrac{1}{3}\\\\\dfrac{a}{3^3}=-\dfrac{1}{3}\\\\\dfrac{a}{27}=-\dfrac{1}{3}\qquad\text{multiply both sides by 27}\\\\a=-\dfrac{1}{3}\cdot27\\\\\boxed{a=-9}[/tex]

Answer:

vertex = ( [tex]\frac{1}{2}[/tex], [tex]\frac{7}{4}[/tex])

Step-by-step explanation:

given a quadratic in standard form : ax² + bx + c : a ≠ 0

the x- coordinate of the vertex can be found as

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

f(x) = x² - x + 2 is in standard form

with a = 1, b = - 1 and c = 2

[tex]x_{vertex}[/tex] = - [tex]\frac{-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]

substitute this value into the function for the y-coordinate

y = ([tex]\frac{1}{2}[/tex])² - [tex]\frac{1}{2}[/tex] + 2 = [tex]\frac{7}{4}[/tex]

vertex = ( [tex]\frac{1}{2}[/tex], [tex]\frac{7}{4}[/tex])

Answer:

h = 3V / lw <===ANSWER

Step-by-step explanation:

V = 1/3 lwh (multiply both sides by 3)

3V = lwh (divide both sides by lw)

3V / lw = h

Answer: The fraction x = 1/2 or its equivalent decimal form x = 0.5

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

Work Shown:

AE = 2*(BD)

4x+8 = 2*(4x+3)

4x+8 = 8x+6

8-6 = 8x-4x

2 = 4x

4x = 2

x = 2/4

x = 1/2

x = 0.5

note: the first equation is set up basically saying that AE is twice that of BD; put another way, BD is half as long as AE. This is one property of midsegments. Another property is that AE and BD are parallel.

another note: if x = 0.5, then AE = 4*x+8 = 4*0.5+8 = 10 while BD = 4*x+3 = 4*0.5+3 = 5, showing that AE is indeed two times longer than BD.

If B and D are midpoints and BD = AE, the lengths BD and AE can be equated. Simplifying the derived equation seems to show a discrepancy suggesting a typo or a misinterpretation in the question.

The problem you're trying to solve involves geometric principles related to midpoints and algebraic concepts. Given that B is the midpoint of segment AC and D is the midpoint of segment CE, we know that BD = AE. Therefore, we can equate the expressions for these segment lengths. This gives us the equation 4x+3 = 4x+8.

To solve for x, we can begin by cancelling out the common terms on both sides, in this case 4x. This simplifies the equation to 3 = 8, which doesn't make sense. This might be an indication of either a typo in the original problem or misinterpretation of the question.

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Answer:

the runner’s pulse will be 70 beats per minute in 7.9 minutes

Step-by-step explanation:

[tex]P(t) = 145e^{-0.092t}[/tex]

Graph the function using a graphing utility.

Graph is attached below.

P(t) is beats per minute

Given P(t) is 70, so we plug in 70 for P(t) and solve for t

[tex]70= 145e^{-0.092t}[/tex]

Divide both sides by 145

[tex]\frac{70}{145} =e^{-0.092t}[/tex]

Now take ln on both sides

[tex]ln(\frac{70}{145})=ln(e^{-0.092t})[/tex]

[tex]ln(\frac{70}{145})=-0.092t[/tex]

Divide both sides by -0.092

So t≈7.91564

Round to nearest tenth t= 7.9

We can verify it from second graph

To find when the runner's pulse will be 70 beats per minute, you need to set the function P(t) = 145e-0.092t equal to 70 and solve for t. This requires knowledge of natural logarithms and exponent laws.

The question asks us to graph the function P(t) = 145e-0.092t which represents a runner’s pulse, P(t), in beats per minute, t minutes after a race where the restriction for the time t is 0 ≤ t ≤ 15. To determine after how many minutes the runner’s pulse will be 70, we can use the equation P(t) and then set P(t) equal to 70, which will look something like this: 70 =145e-0.092t. Solving this equation will therefore give us the time it takes for the runner's pulse to decrease to 70 beats per minute after a race. Solving this requires knowledge of natural log and exponent laws. The resulting value, rounded to the nearest tenth of a minute, should be the correct answer.

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Answer:

-1/5

Step-by-step explanation:

Perpendicular lines are lines which have a specific relationship. The slopes of the two lines are negative reciprocals of each other. We can find the slope easily in slope-intercept form, y=mx+b.

Since our equation is already in slope intercept form then y=5x-2 has a slope of 5.

The slope of the perpendicular line will be -1/5. This is the negative reciprocal of 5.

Answer:

The answer is A, -1/5!

Answer:

$50.40

Step-by-step explanation:

you just add 40% to $36