Answer:
Three consecutive even integers are x, x+2, x+4.
Step-by-step explanation:
Their sum is x+x+2+x+4 = 3x+6.
Hope this helped! <3
Robert accepted a new job at a company with a contract guaranteeing annual raises.
Robert's salary after working for n years can be determined using the equation
S = 5000n + 60000. What is the slope of the equation and what is its
interpretation in the context of the problem?
Answer:
The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.
Step-by-step explanation:
The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Here, given that,
Robert's salary after working for n years can be determined using the equation
S = 5000n + 60000.
Hence, The slope is 5000,
this means that for each additional year Robert works at the company, he earns 5000 more dollars.
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Find mWYZ as well Find mACB please help with both. Thank you every much! Triangles, Need help, right now I’m does adding more stuff so it can stop saying 20 characters.
Answer:
m<WYZ = 23°
m<ACB = 87°
Step-by-step explanation:
Problem 1: Find WYZ
Given,
m<WVX = (3x - 7)°
m<VYZ = (16x - 3)°
∆WYZ ~ ∆WVX, therefore:
m<WYZ = m<WVX (corresponding angles of similar triangles are congruent)
m<WYZ = (3x - 7)° (substitution)
Create an equation to find the value of x.
m<WYZ + m<VYZ = 180° (linear pair)
(3x -7)° + (16x - 3)° = 180° (substitution)
Solve for x
3x - 7 + 16x - 3 = 180
Add like terms
19x - 10 = 180
Add 10 to both sides
19x - 10 + 10 = 180 + 10
19x = 190
Divide both sides by 19
19x/19 = 190/19
x = 10
m<WYZ = (3x - 7)
Substitute x = 10
m<WYZ = 3(10) - 7 = 30 - 7
m<WYZ = 23°
Problem 2: Find m<ACB
Given,
m<A = 62°
m<AED = (11x - 2)°
m<B = (6x + 13)°
∆ADE ~ ∆ACB, therefore:
m<AED = m<B (corresponding angles of similar ∆s are congruent)
(11x - 2)° = (6x + 13)°
Solve for x
11x - 2 = 6x + 13
Collect like terms
11x - 6x = 2 + 13
5x = 15
Divide both sides by 5
5x/5 = 15/5
x = 3
m<ACB + m<B + m<A = 180° (sum of ∆)
m<ACB + (6x + 13) + 62° = 180° (substitution)
Plug in the value of x and solve
m<ACB + (6(3) + 13) + 62° = 180°
m<ACB + (6(3) + 13) + 62° = 180°
m<ACB + (18 + 13) + 62° = 180°
m<ACB + 31° + 62° = 180°
m<ACB + 93° = 180°
Subtract 93 from both sides
m<ACB = 180° - 93°
m<ACB = 87°
Melody is factoring the expression x^3 - 2x^2 + 4x - 8. Her first two steps are shown.
x^3 - 2x^2 + 4x - 8 = x^2(x - 2) + 4(x - 2)
= (x^2 + 4)(x - 2)
What should Melody do next to finish factoring the expression?
A. Melody has completely factored the expression.
B. Melody should rewrite (x^2 + 4) as (x - 2)^2
C. Melody should rewrite (x^2 + 4) as (x - 2)(x + 2)
D. Melody should rewrite (x^2 + 4) as (x + 2)^2
Answer:
A, melody completed factoring
Step-by-step explanation:
Melody has completely factored the expression which is correct option(A).
What is expression?Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given the expression,
⇒ x³ - 2x² + 4x - 8
⇒ x²(x - 2) + 4(x - 2)
⇒ (x² + 4)(x - 2)
So, factors of given expression are (x² + 4) and (x - 2).
Hence, Melody has completely factored the expression.
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How many times greater is the value of the 8 in 38,900 than the value of the 8 in 57,080
it is 100 times greater because it is two places higher than 57,080
On two examinations, you have grades of 87 and 86. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of Ameaning a final average of at least 90 a. What must you get on the final to in the course? b. By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. your final average is less than , you lose your B in the courseDescribe the grades on the final that will cause this to happen
Step-by-step explanation:
We have
87+86+x
T is the total scores
n is number of tests done = 3
T/n is greater than or equal to 90
To get minimum test
T/n = 90
T = 90*n
= 90n
We solve for x
Remember n = 3
90x3 = 270
270 = 87+86+x
270 = 173+x
X = 270-173
X = 97
1.
X = 97
2.
You didn't add a value in your part b question. I used 80 though.
T/n < 80
T<80n
80x3= 240
T<240
87+86+x<240
X<240-173
X<67
X has to be less than 67 so we conclude that if x <=67 b grade will be lost.
Find the volume of the solid under the plane 3x + 5y − z = 0 and above the region bounded by y = x and y = x4.
Answer:
13/18
Step-by-step explanation:
See attachment
Please help
Answer
Answer:
STEP 3.) x = 9/8
Step-by-step explanation:
x + 5/8 = 7/4
x + 5/8 - 5/8 = 7/4 - 5/8
= x =9/8
3. An almirah is sold at 5,225 after allowing a discount of 5%. Find its marked price.
Answer:
4,963.85
Step-by-step explanation:
suppose 123 people voted for danny if 55 of the votes from girls to votes for boys explain
Answer:
Suppose 123 people voted for Danny. If 55 of the votes were from girls, what would be the ratio of votes from girls to votes from boys? If 55 were girls then there were 123-55 = 68 boys. Thus the ratio would be 55 girls to 68 boys, or 55/68.
Answer:
60
Step-by-step explanation:
When Jeremy made 8 black and white copies and 2 color copies at a copy shop, the cost was $1.20. When he made 10 black and white copies and 10 color copies, the cost was $3.00. How much do black and white copies cost?
Answer:
10¢
Step-by-step explanation:
First, to be able to differentiate between the B&W and Color copies, use x in place of the B&W copies and y in place of the Color copies.
Then, write a system of equations to solve (the system of equations input was not working, so there is no brace):
8x + 2y = $1.20
10x + 10y = $3.00
Then, solve the system of equations:
8x + 2y = $1.20
10x + 10y = $3.00
Isolate x to be able to substitute:
8x + 2y = $1.20
8x = -2y + 1.2
x = -2/8y + 1.2/8
x = -0.25y + 0.15
Substitute:
10x + 10y = $3.00
10 (-0.25y + 0.15) + 10y = 3
-2.5y + 1.5 + 10y = 3
7.5y + 1.5 = 3
7.5y = 1.5
y = $0.20
Now that you have the cost of the Colored copies, you can plug it in to find the B&W copies:
8x + 2y = $1.20
8x + 2(0.2) = 1.2
8x + 0.4 = 1.2
8x = 0.8
x = $0.10
What is the equation of the line that passes through the point (-6,-7)(−6,−7) and has a slope of 0?
Answer:
y = -7
Step-by-step explanation:
The equation of a line is:
y = mx + b where m = slope
To find b, plug in a point and solve.
(-6,-7)
y = mx + b
-7 = 0(-6) + b
- 7 = 0 + b
-7 = b
So the equation is:
y = 0x + b or
y = -7
No matter what you plug into x, y = -7, because your slope is 0.
The equation of the line that passes through the point (-6,-7) and with slope 0 is [tex]y=-7[/tex].
Point through which the given line passes ≡ (-6,-7)
The slope of the line =0
What is the equation of a straight line?The equation of a straight line passing through the point (x₁, y₁) is given by: [tex]y-y_1 =m(x-x_1)[/tex]
where m is the slope of the line.
So, the equation of the line that passes through the point (-6,-7) and with slope 0 will be:
[tex]y-(-7) = 0(x-(-7))[/tex]
[tex]y+7 =0[/tex]
[tex]y =-7[/tex]
So, the required equation of the line is y=-7.
Therefore, the equation of the line that passes through the point (-6,-7) and with slope 0 is [tex]y=-7[/tex].
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5x + y =7
20x + 2 = y
Answer:
y = 6
x = 0.2
Step-by-step explanation:
5x + y =7
20x + 2 = y
5x(4) + y(4) = 7(4)
20x + 4y = 28
(20x = 28 - 4y) = (20x = y - 2)
28 - 4y = y - 2
30 - 4y = y
30 = 5y
y = 6
5x + y =7
20x + 2 = y
y = 7 - 5x
7 - 5x = 20x + 2
5 - 5x = 20x
5 = 25x
x = 0.2
A furniture company is producing three types of furniture. Product A requires 7 board feet of wood and 4 lbs of wicker. Product B requires 5 board feet of wood and 5 lbs of wicker. Product C requires 4 board feet of wood and 3 lbs of wicker. There are 3000 board feet of wood available for product and 1400 lbs of wicker. Product A earns a profit margin of $35 a unit, Product B earns a profit margin of $42 a unit, and Product C earns a profit margin of $20 a unit. Formulate the problem as a linear program.
Step-by-step explanation:
this is a linear programming problem, and we are expected to draw up the linear program for the solution of the problem.
The objective function is
Maximize
35A+42B+20C=P
subject to constraints(board and wicker)
The constraints are
board
7A+5B+4C=3000
wicker
4A+5B+3C=1400
A>0, B>0, C>0
The only expression 3(2x+7)-4(-3x+5) is equal (=) to
Answer:
18x + 1
Step-by-step explanation:
3(2x + 7) -4(-3x +5)
6x + 21 + 12x - 20
6x + 12x + 21 - 20
18x + 1
Answer:
18x+1
Step-by-step explanation:
3(2x+7)-4(-3x+5)= 6x+21+12x-20
Combine Like Terms:
6x+12x= 18x
21-20=1
=18x+1
6m + 4n + 3m - 6
What is the expression in simplest form
Mr. Clopu buys an 18-month CD that pays 434% simple interest for $5,000. Find the value of the CD at the end of its term.
Answer:
FV= $5,325.8
Step-by-step explanation:
Giving the following information:
Mr. Clopu buys an 18-month CD that pays 4.34% simple interest for $5,000.
To calculate the future value, we need to use the following formula:
FV= (P*r*t) + P
P= $5,000
r= 0.0434/12= 0.00362
t= 18
FV= [(5,000*0.00362)*18] + 5,000
FV= $5,325.8
The value of the CD at the end of its term is $39,060
Given:
Time = 18 month
Principal = $5000
Interest rate = 434%
Future value = ?
Future value = Principal × Rate × Time
= 5,000 × 434% × 18
= 5000 × 434/100 × 18
= 5000 × 4.34 × 18
= 39,060
Therefore, the value of the CD at the end of its term is $39,060
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Steven earns extra money babysitting. He charges $34.50 for 6 hours and $46.00 for 8 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
Answer:
y = 5.25x + 4
Step-by-step explanation:
(hours, money)
(6, 34.50)
(8, 46.00)
Slope: change in y/change in x
11.5/2
5.25
Y - intercept: b
46 = 5.25(8) + b
46 = 42 + b
4 = b
Put it all together
Determine the equation of a circle with center (5,-3) and radius of 9
Step-by-step explanation:
solve by using the formula
The required equation of a circle with a center (5, -3) and radius of 9 is x² + y² -10x + 6y - 48 = 0.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
As in the mentioned question,
center (5,-3) and radius is 9,
(x - h)² + (y - k)² = r²
(x - 5)² + (y +3)² = 9²
x² + y² -10x + 6y - 48 = 0
Thus, the required equation of a circle with a center (5, -3) and radius of 9 is x² + y² -10x + 6y - 48 = 0.
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1.a) Convert 81° into grade.
10
Step-by-step explanation:
I hope it helps man this much .
Cliff needs 6 meters of wood for a building project. He already has 3
meters of wood.
Approximately how many feet of wood does Cliff need? (One meter
is approximately 3.3 feet.)
1 foot
03 feet
O 6 feet
10 feet
Help plzzz
Answer:
3 meters or 9.9 feet rounded up is 10 feet because they only sell wood by the foot.
Step-by-step explanation:
6 meters - 3 meters = 3 meters
1meter = 3.3 feet
3 meters x 3.3ft = 9.9 feet
What is 1047.04 divided by 16
Answer:
D
Step-by-step explanation:
Cause the calculator says so...
Answer:
65.44
Step-by-step explanation:
I copied and pasted but this is the answer 65.44
plz help me out with this idk if i did it right<3
Answer:
The first and third ones are correct
Step-by-step explanation:
Hope this helps (:
Answer:
The 4th and 5th one seem to be correct.
What is
What is the measure of angle B?
A. 30°
C. 35°
Answer:
A
Step-by-step explanation:
Give 3 names for x intercepts of a quadrants equation
Answer:
Zeros
Roots
Solution (Set)
Step-by-step explanation:
As you can tell there are a handful of different names!
The value is directly proportional to the value of x. If y =102 when x = 6, what is the value of y when x= 24
Answer:
y=408
Step-by-step explanation:
y is directly proportional to x
y=kx (where k is the constant)
102=6k
102÷6=k
17=k
y=17x
find y when x=24
y=17(24)
y=408
The selling price of a car is $11,000. Each year, it loses 17% of its value.Find the exponential function that gives the value of the car t years after its purchase. Write your answer in the form f(t)=a(b)t.
Answer:
The answer is "[tex]\bold{11000(0.83)^t}[/tex]".
Step-by-step explanation:
[tex]\bold{ \text{selling price}} = \$ 11,000 \\\\\bold{ \text{loses}} = 17 \%[/tex]
[tex]\bold{\to f(t)= c (1-r)^t} \\\\[/tex]
[tex]=11,000 (1- 0.17)^t\\\\=11,000(0.83 )^t[/tex]
A store has 2 times as hooded sweatshirt as crewneck sweatshirts. The total number of sweatshirts is 36. How many hooded sweatshirts does the store have?
Answer:
Answer below
Step-by-step explanation:
It would be 36×2=72
since we're doubl8ng it so there would be 72 hooded sweatshirts
Answer:
24 Hooded Sweatshirts
Step-by-step explanation:
36/3=12
2x12=24 or hooded sweatshirts
1x12=12 or crewneck sweatshirts
12+24=36 total sweatshirts :)
evaluate 292.4 divided by 17.
THANK YOU! :)
Answer:
17.2
Step-by-step explanation:
The coordinates below lie on the line with the given slope. find the missing coordinate value. (2,2) (5,y) slope = 2
Step-by-step explanation:
Hey there!
The given points are; (2,2) and (5,y).
Slope (m) =2
Using formula for slope, we get;
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Put all values.
[tex]2 = \frac{y - 2}{5 - 2} [/tex]
Simplify it to get value of"y".
[tex]2 = \frac{y - 2}{3} [/tex]
[tex]6 = y - 2[/tex]
[tex]y = 6 + 2[/tex]
Therefore, y= 8.
Hope it helps...
mental math again 60x40x2
Answer:
the answer is 4800
Answer:
What is mental math?
Mental math is definitely what it sounds like—doing math in your head. But it’s also more nuanced than that. Being good at mental math tricks doesn’t mean that you’re able to solve 8974387 x 396 in your head instantly; while cool, that wouldn’t be very practical for daily life. So what does mental math mean?
It really just means being able to calculate in your head. It doesn’t mean you can solve every type of problem every time, nor is it a skill that you either “have” or “don’t have”; it’s a skill that you can learn, practice, and improve so that you can solve a bigger range of problems. And mental math certainly doesn’t have to be entirely in your head, either. Jotting down the numbers you need to remember to give you a head start (no pun intended), or writing down your solutions at each “step,” does not negate the “mental”-ness of the math.
Is mental math useful?
Ask this question again next time you’re trying to figure out a tip or doing any kind of construction or home improvement project! And, in addition to handy practical uses, knowing how to do mental math can also just keep your brain sharp and curb your reliance on calculators. Because, come on, doesn’t it feel good to reach for a calculator only to realize, “Wait, I don’t need it!” and figure out the answer in your head? (Spoiler: It does!) Not to mention knowing how to mentally solve small, simple math problems can save you some steps and help you out if you do need to solve a more complicated, difficult problem. There are always going to be some math problems that it would be silly to not solve with a calculator, but, yes, mental math is useful. And if you’re wondering if math itself is useful, math lessons you’ll actually use in real life.
Step-by-step explanation: