Solve using substitution

Answers

Answer 1

The first step is to isolate one of the variables from one of the equations. We can pick either variable and either equation. The easiest to pick on is the 'x' from the first equation as the coefficient here is 1.

Isolate x in the first equation. Subtract 3y from both sides
x+3y = 8
x+3y-3y = 8-3y
x = 8-3y
So we can see that x is the same as 8-3y

Now move onto the second equation
3x - 5y = -18
3( x ) - 5y = -18 ... rewrite x so it has parenthesis around it
3( 8-3y) - 5y = -18 ... replace x with 8-3y; solve for y
24-9y - 5y = -18
24-14y = -18
24-14y-24 = -18-24
-14y = -42
-14y/(-14) = -42/(-14)
y = 3

If y = 3, then x is...
x = 8-3y
x = 8-3*3
x = 8-9
x = -1

The x and y values are x = -1 and y = 3
Together they pair up to form the ordered pair (x,y) = (-1,3)

The solution is (-1,3)
If you graph the two original lines, then they cross at (-1,3)

Related Questions

20 Points!!!
For working 13 hours you earned $45.50 and $94.50 for 27 hours. What is your rate of pay in dollars per hour? a. 14 dollars per hour b. 3.50 dollars per hour c. 6.50 dollars per hour d.2.07 dollars per hour

Will give branliest!!!
Help ASAP.

Answers

B 3.5 dollar per hour

Answer:

$3.50 per hour

Step-by-step explanation:

Given : For working 13 hours you earned $45.50 and $94.50 for 27 hours

To Find :What is your rate of pay in dollars per hour?

Solution :

Pay for 13 hours = $45.50

So, Pay for 1 hour = [tex]\frac{45.50}{13}[/tex]

Pay for 1 hour = [tex]3.50[/tex]

So, rate is $3.50 per hour

So, Option B is true

Hence rate of pay in dollars per hour is $3.50 per hour

true or false 120% of a whole number is always greater than the number? and why?

Answers

I can only use math to explain it. What is 100%?
100% = [tex] \frac{100}{100}[/tex]
percent means per 100.
so 120% = 120/100 = 1.2
120% of a whole number. For example 120% * 10 = [tex] \frac{120}{100} * 10 [/tex] = 12
is it greater than 10.

Since whole numbers are positive integers, then it follows that a positive integer multiplied by 1.2 will be greater than the original by 20%.

Sammy is 5 feet 3 inches tall. He casts a shadow that is 31 feet 6 inches long. He is standing next to a stop sign that casts a shadow that is 40 feet 6 inches long. How tall is the stop sign in feet and inches.

Answers

Both Sammy and the stop sign form right angles with the ground. They also have the same angle of depression, where the sun hits them and casts their shadows. This means the third angle of each triangle must be congruent as well. Therefore the triangles will be similar. Since they are similar, we will use a proportion to solve this problem. First I convert the feet and inches to only inches. 5 ft 3 in = 63 in; 31 ft 6 in = 378 in; 40 ft 6 in = 486 in. The proportion will then be
[tex]\frac{378}{486}=\frac{63}{x}[/tex]. This comes because we compare corresponding sides of the similar triangles. 378 corresponds with 486, since they are the horizontal lengths of the shadows. 63 corresponds to x, since they are the heights of Sammy and the sign. Solving this by cross multiplication:
[tex]378*x=63*486 \\378x=30618[/tex]
Divide both sides by 378:
[tex]\frac{378x}{378}=\frac{30618}{378} \\x=81[/tex]
The sign is 81 inches tall. Converting this to feet and inches, divide by 12; this gives us 6.75. We have 6 feet and 0.75 feet. 0.75 feet * 12 inches per foot = 9 inches. The sign is 6 feet 9 inches tall.

abcd is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC s 4y-6 and the length of CD is 8y-18, find the value of y. 30 points for brainliest!

Answers

We are told that the legs of the isosceles trapezoid are AB and CD

AB = 7y - 4
CD = 8y - 18

In any isosceles trapezoid, the two legs are of equal length.
Therefore, AB = CD

⇒ 7y - 4 = 8y - 18

Add 18 to both sides of the equation
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y

Subtract 7y from both sides of the equation
7y - 7y + 14 = 8y - 7y
14 = y
⇒ y = 14

The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.

Given :

ABCD is an isosceles trapezoid with legs AB and CD and base BC.If the length of AB is (7y - 4), the length of BC s (4y - 6) and the length of CD is (8y - 18).

The two legs are of equal length In any isosceles trapezoid that means:

7y - 4 = 8y - 18

Add 18 on both sides in the above equation.

7y - 4 + 18 = 8y - 18 + 18

7y + 14 = 8y

Now, subtract 7y on both sides in the above equation.

7y + 14 - 7y = 8y - 7y

Simplify the above expression in order to get the value of 'y'.

y = 14

For more information, refer to the link given below:

https://brainly.com/question/19273676

45% of 40 is 18% of what number?

Answers

Answer:

45% of 40 is 18% of 100

Step-by-step explanation:

45% of 40 is 18% of what number

First we find out what is 45% of number 40

45% times 40

[tex]\frac{45}{100} * 40= 18[/tex]

Now we find

18 = 18% of what number

Let the unknown number be x

18 = 18% * x

[tex]18= \frac{18}{100} * x[/tex]

18 = 0.18 * x

Divide by 0.18 on both sides

100= x

So 45% of 40 is 18% of 100

The complete statement is 45% of 40 is 18% of 100

How to determine the number that completes the statement

From the question, we have the following parameters that can be used in our computation:

45% of 40 is 18% of what number

Represent the number with x

So, we have

45% of 40 is 18% of x

Express as an equation

45% of 40 = 18% of x

Next, we have

18 = 0.18x

Divide through by 0.18

x = 100

Hence, 45% of 40 is 18% of 100

Answers

Final answer:

When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.

Explanation:

The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.

Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.

Learn more about Volume of a cylinder here:

https://brainly.com/question/16788902

#SPJ12

The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]

Let's analyze the relationship between the volume of a cylinder and its dimensions.

The volume [tex]$ V $[/tex] of a cylinder is given by the formula:

[tex]\[ V = \pi r^2 h \][/tex]

where:

[tex]$ r $[/tex] is the radius of the cylinder,

[tex]$ h $[/tex] is the height of the cylinder.

Given that the height [tex]$ h $[/tex] remains unchanged, if the radius [tex]$ r $[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]$ r' $[/tex] becomes[tex]$ 5r $.[/tex]

Now, let's compare the volumes before and after the increase in radius:

1. Original Volume [tex]($ V_{\text{original}} $)[/tex]

[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]

2. New Volume [tex]($ V_{\text{new}} $)[/tex]

After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]$ r' = 5r $[/tex].

[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]

Now, compare [tex]$ V_{\text{new}} $[/tex] with [tex]$ V_{\text{original}} $[/tex]

[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]

help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.

A. x=2, y=1

B. x=3, y=2

C. x=1, y=2

D. x=2, y=3

Answers

according to the HL theorem for right-triangles, one leg and the hypotenuse must be equal, what does that mean?

well it means that 3y = x + 3, and that y + 1 = x, when does that happen anyway? let's see,

[tex]\bf \begin{cases} 3y=x+3\\ y+1=\boxed{x} \end{cases}\implies 3y=\boxed{y+1}+3\implies 3y=y+4 \\\\\\ 2y=4\implies y=\cfrac{4}{2}\implies y=2\\\\ -------------------------------\\\\ \textit{and since we know that }y+1 =x\implies (2)+1=x\implies 3=x[/tex]

A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone?

Answers

Cylinder Volume = PI * radius^2 * height
Cylinder Volume = 3.14159 * 1 * 21
Cylinder Volume = 65.97 cc

Volume Cone = [PI * radius^2 * height] / 3
radius^2 = 3 * 65.97 / (3.14159 * 7)
radius^2 = 9
radius = 3 centimeters

The radius of the cone is 3 cm.

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.

y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)

Answers

Writing [tex]5x-2y=-6[/tex] in slope-intercept form:

[tex]5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3[/tex]

The slope of the line is the number before "x", which is [tex]\frac{5}{2}[/tex].

The slope of the perpendicular to this line is the negative reciprocal of this.

So the slope of perpendicular is [tex]-\frac{2}{5}[/tex].

To find the equation of the perpendicular line, we need a point. It is given as [tex](5,-4)[/tex] where [tex]x_{1}=5[/tex] and [tex]y_{1}=-4[/tex].

Now we use the point-slope form of a line to figure out the equation:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Plugging in the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and [tex]m=-\frac{2}{5}[/tex], gives us:

[tex]y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2[/tex]

Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:

[tex]y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10[/tex].

THIS IS THE SECOND OPTION.

ANSWER: [tex]2x+5y=-10[/tex]

What's the explicit formula HELP

Answers

replace N with 6

6(6+1)(2(6)+1) / 6

(6*7*13) / 6

546 / 6 = 91

Answer is C

Information is given about a polynomial f left parenthesis x right parenthesisf(x) whose coefficients are real numbers. find the remaining zeros of f. degree 3; zeros: negative 8 comma negative 3 minus i−8, −3−i enter the remaining zeros of f.

Answers

A polynomial with real coefficients has either real zeros or conjugate pairs of complex zeros. A degree-3 polynomial will have 3 zeros. The one not listed is the conjugate of the complex zero listed.

The remaining zero of f(x) is -3+i.

If you answer (making sense) and explain (so I can understand) you will be awarded! Please help ASAPA

Answers

What you are doing is called cross multiplication. You have to multiply the top of the first fraction by the bottom of the second fraction. 1 x 378, which equals 378. Then you multiply the bottom of the first fraction by the top of the second fraction. 250 x X. 250x=378. You then have to solve for x or divide 378 by 250. The answer to 378 / 250 = 1.512. But the instructions want you to round to the nearest tenth and that is the first decimal place. Your answer is 1.5.

what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?

A)Reflected over the x-axis and rotated 180 degrees

B)Reflected over the y-axis and rotated 180 degrees

C)Reflected over the x-axis and rotated 90 degrees counterclockwise

D)Reflected over the y-axis and rotated 90 degrees counterclockwise

Answers

Rectangle ABCD has vertices A(-4,2), B(-4,1), C(-1,1) and D(-1,2).

1. Apply the reflection over the x-axis that has a rule

(x,y)→(x,-y).

Then

A(-4,2)→A''(-4,-2);B(-4,1)→B''(-4,-1);C(-1,1)→C''(-1,-1);D(-1,2)→D''(-1,-2).

2. The second transformation is rotation by 90° counterclockwise about the origin. This transformation has a rule

(x,y)→(-y,x).

Then

A''(-4,-2)→A'(2,-4);B''(-4,-1)→B'(1,-4);C''(-1,-1)→C'(1,-1);D''(-1,-2)→D'(2,-1).

As you can see these points are exactly those frome the diagram.

Answer: 1st transformation is reflection over the x-axis and second transformation is rotation by 90° counterclockwise about the origin.

Evaluate the exponential expression. Write your answer as a fraction in simplest form.

(2^3)^-2

Answers

Hey there! :D

(2^3)^-2

Multiply the powers.

2^-6

Put the negative on the bottom.

1/2^6

1/64= the equivalent fraction

I hope this helps!
~kaikers

How long will it take for 750 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 68 mg?

A. ≈ 50 days
B. ≈ 54 days
C. ≈ 48 days
D. ≈ 52 days

Answers

For this case we have an equation of the form:
y = A (b) ^ t
Where,
A: initial amount
b: decrease rate
t: time
Substituting values:
y = 750 (0.5) ^ ((1/15) * t)
The number of days to reach 68 mg is:
68 = 750 (0.5) ^ ((1/15) * t)
Clearing t:
(0.5) ^ ((1/15) * t) = (68/750)
log0.5 ((0.5) ^ ((1/15) * t)) = log0.5 (68/750)
(1/15) * t = log0.5 (68/750)
t = 15 * log0.5 (68/750)
t = 51.94
Rounding:
t = 52 days
Answer:
D. ≈ 52 days

Answer:

52 Days

Step-by-step explanation:

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:

© 2011 Jupiterimages Corporation

Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
68.3
38.4
268.8
230.4

Answers

Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s

The answer is 268.8 (third one) just took the quiz

A flower garden is in the shape of a right triangle. One leg of the triangle is 6 ft long and the hypotenuse is 12 ft long. What is the length of the other leg?

answers
A. 10.4ft
B.12.8ft
C13ft
D14.6ft

Answers

I believe the correct answer is A 10.4 feet long.
If this answer helped you and was correct you can name me "Brainliest." ty :)

The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.

Identify the population and the sample

a.

population: 1,000,000 cartons of eggs

sample: every 50th carton in each shipment

c.

population: 10 shipments of 1000 cartons of eggs

sample: every 50th carton in each shipment

b.

population: 1,000,000 cartons of eggs

sample: the 50th carton of eggs

d.

population: 10 shipments of 1000 cartons of eggs

sample: the 50th carton of eggs

Answers

10 times 1000 is 10,000, not 1,000,000. So, option A and B can be immediately eliminated, and since the question say every 50th carton, I think the answer is C.

Answer:

Option c. Population: 10 shipments of 1000 cartons of eggs

sample: every 50th carton in each shipment.

Step-by-step explanation:

First we find out population :

For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.

Therefore, 1000 × 10 = 10,000 cartons of eggs.

Population : 10,000 cartons of eggs

Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.

Hence, Sample would be every 50th carton in each shipment.

In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs

Therefore, option c would be correct.

In 1985, there was 285 cell phones subscribers in the small town of centerville.After 1985, the number of subscribers increased by 75% per year. How many cell phones subscribers were in centerville in 1994 ?

Answers

First we write a function that suits the problem.
We have then:
y = 285 * (1.75) ^ x
Then, we see how many years there are in the requested period
x = 1994-1985 = 9
We evaluate the function for x = 9
y = 285 * (1.75) ^ 9
y = 43871.98637
Round nearest whole number
y = 43872
Answer:
there were 43872 cell phones subscribers in centerville in 1994

Can someone help me please?

Answers

I'm thinking its the answer is B

check the picture below.

now, notice Thales theorem on the semi-circle, therefore, IF those two segments in the semi-circle, namely TQ and TS, are indeed perpendicular, that means the angle at the vertex T is a right-angle, and by Thales theorem, QS must be the diameter.

Which of the following is a cubic binomial
A.w^3-6w^2+9
B.7a^3+4a^-2
C.-y^3+3y^5
D.x^2-2x^3

Answers

the answer is B.
this is because it has two terms, and the first term has a power of 3

Solve for x
Please help quick

Answers

a and b are perpendicular meaning that they intersect forming 90
b and c are parallel meaning that the intersection of c and a is also perpendicular

11x - 9 = 90 degrees
solve
11x - 9 = 90
add 9 to both sides
11x = 99
divide both sides by 11
x = 9

Hope this helps

The Art Store sells three types of art pencil sets. The profit is $8.45 on watercolor pencil sets, $6.19 on pastel pencil sets and $4.62 on charcoal pencil sets. There are two branches of the Art Store. The number of sales of pencil sets for each store are shown in the table below.

Set Type
Sales for Westside Branch
Sales for Downtown Branch
watercolor
132
74
pastel
56
48
charcoal
119
126

Which store had the most profit and what was the total profit of that store?

Answers

Sales for Westside Branch
watercolor
132*(8.45)=1115.4
pastel
56*(6.19)=346.64
charcoal
119*(4.62)=549.78
Total profit= 1115.4 + 346.64 + 549.78 = 2011.82

Sales for Downtown Branch
watercolor
74*(8.45)= 625.3
pastel
48*(6.19)= 297.12
charcoal
126*(4.62)= 582.12
Total profit= 625.3 + 297.12 + 582.12 = 1504.54

Answer:
Westside Branch had the most profit and the total profit of that store was
2011.82$

Answer:

Step-by-step explanation:

Which of these states had a flat state income tax in 2009

Apex
A.Michigan
B.New Hampshire
C.South Carolina
D.Georgia

Answers

the answer would have to be Michigan. They had a flat income tax in 2009

Answer:

The correct answer is:

Michigan.

Michigan is the state that had a flat state income tax in 2009.

Step-by-step explanation:

A flat tax (short for flat-rate tax) is a tax system with a constant marginal rate, usually applied to individual or corporate income.

Flat tax benefits higher income brackets progressively due to decline in marginal value.

The state that had a flat state income tax in 2009 is:

Michigan.

Michigan is a flat-tax state that levies a state income tax of 4.25%

Solve y=x^2 + 7 for x

Answers

Hello! To solve for x means to isolate x:

y = x^2 + 7
y - 7 = x^2
sqrt(y - 7) = x

Answer:
x = sqrt(y - 7)

Hope this helps!

Final Answer:

The solutions to the equation [tex]$ y = x^2 + 7 $[/tex] for x are: [tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]

Explanation:

To solve the equation [tex]$ y = x^2 + 7 $[/tex] for x, you want to isolate x on one side of the equation. Here are the steps to do so:
1. **Subtract 7 from both sides**:
To isolate the [tex]$ x^2 $[/tex] term, we first remove the constant term on the right side by subtracting 7 from both sides of the equation.
[tex]$ y - 7 = x^2 + 7 - 7 $[/tex]
This simplifies to:
[tex]$ y - 7 = x^2 $[/tex]

2. **Take the square root of both sides**:
To solve for x, you need to get rid of the square on the x term. This is done by taking the square root of both sides. Remember that when you take the square root of both sides of an equation, you must consider both the positive and negative square roots.
[tex]$ \sqrt{y - 7} = \pm\sqrt{x^2} $[/tex]

Simplifying the right side (since the square root and square operations are inverses of each other), we get:
[tex]$ \sqrt{y - 7} = \pm x $[/tex]

3. **Solve for x**:
We now have two solutions for x, a positive and a negative one, because squaring a positive or a negative number both give a positive result. Therefore, we write:

[tex]$ x_1 = +\sqrt{y - 7} \\\\ \( x_2 = -\sqrt{y - 7} $[/tex]

So, the solutions to the equation [tex]$ y = x^2 + 7 $[/tex] for x are:

[tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]

Remember that you can only take the square root of a non-negative number in real numbers. So if y - 7 is negative, the solutions for x would be complex numbers.

https://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS9/9.029.png

Answers

Answer:

x = 14

x = negative 2

x = 2

x = negative 14

Step-by-step explanation:

Assume that the grasshopper in the food pyramid above must eat half its body weight in grass each day. If an average-size grasshopper weighs 2 grams, and 1 blade of grass weighs 0.1grams (one tenth of a gram), how many blades of grass does the grasshopper need to eat each day?

Answers

The first thing we need to know is how much grass the grasshopper needs to eat.
We have:
"must eat half its body weight in grass each day":
(2 grams) * (1/2) = 1 gram
Then,
"1 blade of grass weighs 0.1grams"
Then the amount you need to eat is given by:
N = (1) / (0.1)
N = 10 blades of grass
Answer:
the grasshopper needs to eat 10 blades of grass each day

Answer:

The grasshopper needs to eat 10 blades of grass each day.

Step-by-step explanation:

The grasshopper in the food pyramid above must eat half its body weight in grass each day.

The average weight of the grasshopper is 2 grams.

The weight of one blade of grass is 0.1 grams.

Now,

The weight of grass eating by the grasshopper per day is 1 gram.

Let us assume that the grasshopper eats the "n" number of blades of the grass.

Therefore,

[tex]\begin{aligned}n \times 0.1\;\rm{gm}&=1\;\rm{gm}\\n&=\dfrac{1}{0.1}\\n&=10\end{aligned}[/tex]

To know more, please refer to the link:

https://brainly.com/question/19043537?referrer=searchResults

Zaira spent 55 hours in 2 weeks working on a science project. she worked 32 hours the first week. Write and solve an addition equation to find the amount of time she spent working the second week.

Answers

what do we know?
55 hours in 2 weeks
32 hours in the first week
So, 32 plus the amount of time she worked on the project the second week adds up to 55.
32 + x = 55
Now, simply solving! What you do to one side, you do to the other in order to isolate the variable
(32 - 32) + x = (55 - 32)
x = 23
She worked 23 hours on the project during the second week!

What is the vertex of the parabola?

A. (-1,0)
B. (0,-3)
C. (1,-4)
D. (3,0)

Answers

The vertex of a parabola is its highest or lowest point. Here, it is the lowest point, which happens right at the bottom of the U-shape—at (1, –4). Therefore, the answer is C.

Option C is correct, the vertex of the parabola is (1, -4).

What is Conic section?

Any curve produced by the intersection of a plane and a right circular cone is called as Conic section.

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.

In this case, since the parabola opens upward, we can see that

the vertex is the lowest point on the parabola which is (1,-4).

Hence, Option C is correct, the vertex of the parabola is (1, -4).

To learn more on Conic section click:

https://brainly.com/question/28991363

#SPJ3

the law of cosines is used to find the value of m. m2 = 272 + 182 ??? 2(27)(18)cos(28??) m2 = 729 + 324 ??? (972)cos(28??) m2 = 1053 ??? (972)cos(28??) To the nearest whole number, the value of m is .

Answers

we know that

the law of cosines establishes:

c² = a² + b² - 2 ab cos C

in this problem

a=27

b=18

C=28°

c=m

m² = 27² + 18² - 2*(27)*(18)* cos(28°)

m² = 729 + 324 - 972* cos(28°)

m² = 1053 - 972* 0.8829

m² = 194.82-------------> m=13.96-----------> 14

the answer is m=14 units

Other Questions