Answer:
Step-by-step explanation:
Estimated the difference
645,908 + 335,297
_ - _ = _
if pictures width 4+w and the length measures 8w+2, how much longer is the picture than it is wide?
The picture is 7w - 2 units longer than it is wide, this is found by subtracting the width (4+w) from the length (8w+2).
To find out how much longer the picture is than it is wide, we must compare the picture's length and width. Given the picture's width is 4+w and the length is 8w+2, we subtract the width from the length to find the difference:
Length - Width = (8w+2) - (4+w) = 8w + 2 - 4 - w = 7w - 2.
Therefore, the picture is 7w - 2 units longer than it is wide.
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Jimmy is going to pack his backpack for a trip. His backpack is 60 cubic litres. He has a pile of equipment that takes up 43 cubic litres and then he has his sleeping bag that takes up 23 cubic litres. Let r be the amount of room left in his backpack. Which equation could you use to determine if he has enough room in his backpack.
A) r = 23 + 43
B) r = 23 + 43 + 60
C) 23 + 43 + r = 60
D) 23 + r = 60 + 43
The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.
Given that, Jimmy backpack is 60 cubic liters. He has a pile of equipment that takes up 43 cubic liters and then he has his sleeping bag that takes up 23 cubic liters.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let r be the amount of room left in his backpack.
Total space in backpack = A pile of equipment + Sleeping bag + Room left
So, 60 = 43+23+r
The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.
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find the measure of <ghk <hki and <hkj show your work or wite and explanation
In the circle graph above, you can see that 47% of the company's monthly income is used to pay the owner's personal salary. If the amount of the owners's personal salary was $2,176.10 this month, what was the company's total monthly income this month?
Final answer:
To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.
Explanation:
In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.
9+(6-6)x4-(-7-(-2)) solved in order of operations
Janelle has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph how long should she plan to spend walking back?
Final answer:
Janelle should plan to spend 3 hours walking back.
Explanation:
To find out how long Janelle should plan to spend walking back, we need to calculate the total time it takes her to run and walk. Since she runs at a speed of 7mph, she completes the distance of the race in 1 hour (4 miles / 7mph = 0.57 hours = 1 hour). Therefore, she spends 1 hour running and 3 hours left for walking. To find out the distance she walks back, we use the formula distance = speed x time. Since she walks at a speed of 3mph, the distance she walks back is 3mph x 3 hours = 9 miles.
What is the factorization of g3 – 125?
(g– 5)(g2 + 5g + 10)
(g – 25)(g2 + 25g + 625)
(g – 5)(g2 + 5g + 25)
(g – 25)(g2 + 5g + 125)
Answer: (C) (g – 5)(g2 + 5g + 25)
Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution
Answer:
[tex]x=\frac{225}{16}[/tex] is an extraneous solution.
Step-by-step explanation:
Given : Equation [tex]-4\sqrt x-3=12[/tex]
To find : Solve for x and identify if it is an extraneous solution?
Solution :
Step 1 - Write the equation,
[tex]-4\sqrt x-3=12[/tex]
Step 2 - Add 3 both sides,
[tex]-4\sqrt x-3+3=12+3[/tex]
[tex]-4\sqrt x=15[/tex]
Step 3 - Squaring both sides,
[tex](-4\sqrt x)^2=(15)^2[/tex]
[tex]16x=225[/tex]
Step 4 - Divide both side by 16,
[tex]\frac{16}{16}x=\frac{225}{16}[/tex]
[tex]x=\frac{225}{16}[/tex]
For extraneous solution, Substitute the value of x back in the equation.
[tex] -4\sqrt (\frac{225}{16})-3=12[/tex]
[tex]-4\times\frac{15}{4}-3=12[/tex]
[tex]-15-3=12[/tex]
[tex]-18\neq12[/tex]
The value of x does not satisfy the equation which means the value of x is an extraneous solution.
So, [tex]x=\frac{225}{16}[/tex] is an extraneous solution.
Over the last three evenings, Latoya received a total of 79 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?
Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula mc024-1.jpg for payment, m, which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B
To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.
Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.
Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:
m = P[r(1+r)^n] / [(1+r)^n-1]
Where:
Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.
After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.
The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?
Answer:
the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)
Step-by-step explanation:
The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]
The parent function is f(x)=x^2
Now we compare parent function f(x) and g(x)
In g(x), negative sign at first
f(x) ----> -f(x) , the graph is reflected across x axis
f(x)-----> f(x-h), the graph will be transformed h units to right
f(x)----> f(x) +k , the graph will be transformed k units up
[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)
(algebra)
Solve for x.
Fx-gx=h
If we solve the equation which is (F × x ) - (g × x ) = h , we will get the value of x as x = h / ( F - g ).
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
An equation is given which is :
(F × x ) - (g × x ) = h
We have to solve this equation to get the value of the variable x.
So, the value of x can be calculated as :
(F × x ) - (g × x ) = h
Taking common x from LHS :
x ( F - g ) = h
Dividing by ( F - g ) on both sides we get :
[ x ( F - g ) / ( F - g )] = h / ( F - g )
or
x = h / ( F - g )
Therefore , if we solve the equation which is (F × x ) - (g × x ) = h , we will get the value of x as x = h / ( F - g ).
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Felicity is placing a rectangle in the coordinate plane. She knows that the longer side of the rectangle is 3 times its shorter side. She places the longer side on the x-axis.
What coordinates should she assign to the top-right vertex of the rectangle?
Answer:
(3a,a)
Step-by-step explanation:
As you know the component on the X vertex is the first that is represented when setting point coordenates, and the second value is in the Y vertex, as you can see the value for Y is a, and in the problem says that the longer side is three times the short side, since the Y vertex is the short side, that means the X vertex will have the longer side, making it 3a. So the coordenates will be (3a,a).
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Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $50 and costs an additional $0.13 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?
Hannah travels 6 times as many minutes than Raoul does. Together, they travel 63 minutes. How many minutes does Hannah travel? Draw a model and wrote an equation to solve.
The graph shows a line and two similar triangles.
Answer:
Option C. is the correct option.
Step-by-step explanation:
The given line in the graph passes through two points (0, 3) and (3, 7).
We have to find the equation of the line.
Since y = mx + c is the standard equation of a line
where m = slope of the line
c = y - intercept
Slope of a line m = [tex]\frac{(y-y')}{(x-x')}[/tex]
Now we put the values of x and y to find the slope of this line.
m = [tex]\frac{7-3}{3-0}=\frac{4}{3}[/tex]
Since (0, 3) passes through the line
3 = 0 + c
c = 3
Equation of the line will be
[tex]y=\frac{4}{3}x+3[/tex]
Option C. is the answer.
Answer:
me dony know
Step-by-step explanation:
P(-9,1);m=1 use slope intercept form to write an equation of a line passing through the given point and having the given slope. Express answer in Standord form
9.17/15.00
Is this a A+ or A or B or C
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2) = ?
what is the greatest common factor of 15 and 27
Final answer:
The greatest common factor of 15 and 27 is 3, which is the largest number that divides both numbers without a remainder.
Explanation:
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 15 and 27, list the factors of each number:
Factors of 15: 1, 3, 5, 15
Factors of 27: 1, 3, 9, 27
The common factors of 15 and 27 are 1 and 3. The largest of these is 3, therefore the greatest common factor of 15 and 27 is 3.
What is the unit rate of 15 degrees in 2 hours.
Which linear system has a solution of
[tex]x = 2 \: and \: y = - 3[/tex]
What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16
Answer:
y = 8Step-by-step explanation:
[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]
[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]
[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]
[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]
Answer:
6
Step-by-step explanation:
Ben earns $1500 each summer and puts the money in a savings account with a 6% simple interest rate. If he deposits the same amount each year, how much money will he have at the end of his third summer
$4770
$3250
$3175
$2850
The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. the life of this bulb is normally distributed. what is the probability that a randomly selected bulb would last longer than 1150 hours?
write a comparison sentence to resent this equation 6 times 7 equals 42
A comparison sentence for the equation '6 times 7 equals 42' using multiplication.
Comparing the given equation '6 times 7 equals 42' using a sentence:
In comparison to the equation 6 times 7 equals 42, the sentence '7 multiplied by 6 results in 42' represents the relationship between the factors and the product.
What is a distributive property of 72 divided by 4
Answer:
[tex]\frac{72}{4}=18[/tex]
Step-by-step explanation:
To find : What is a distributive property of 72 divided by 4 ?
Solution :
The distributive property of division is given by,
[tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]
We have to divide 72 by 4,
So, Re-write 72 as 60+12.
Substitute,
[tex]\frac{72}{4}=\frac{60+12}{4}[/tex]
[tex]\frac{72}{4}=\frac{60}{4}+\frac{12}{4}[/tex]
[tex]\frac{72}{4}=15+3[/tex]
[tex]\frac{72}{4}=18[/tex]
Therefore, [tex]\frac{72}{4}=18[/tex]
While the distributive property is typically relevant for multiplication over addition or subtraction, you can apply it to division by first rewriting the division as multiplication by the reciprocal. For example, 72 divided by 4 can be rewritten as 72 times 1/4, and then distributed over a sum or difference.
Explanation:The distributive property involves multiplication and addition or subtraction, not division. However, if we interpret your question in a bit different way, we can make use of the distributive property for division. To start, dividing 72 by 4 is the same as multiplying 72 by 1/4. So, we can rewrite it as follows:
72 * 1/4
The distributive property is applied when you multiply a number by a sum or a difference. For example, in case of [tex]72*1/4 = (40+32)*1/4[/tex], it would distribute as: [tex]40*1/4 + 32*1/4[/tex]. It gives us 10 + 8 = 18 which is the correct answer. This way, the distributive property can be used in division if the division is expressed as a multiplication.
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Which equation represents a line that passes through (–9, –3) and has a slope of –6?
If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear
If Sam has 6 different hats and 3 different scarves, the number of combinations he could wear is: 18 ways.
Given the following data:
Number of hats = 6 hats.Number of scarves = 3 scarves.How to determine combinations.In this exercise, the number of ways 6 different hats and 3 different scarves can be worn without any form of repetition should be calculated by using a combination.
Mathematically, combination is given by this formula:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Where:
n is the number of items.r is the number of times of choosing items.For Sam's combination:
[tex]_hC_s = 6 \times 3[/tex]
Sam = 18 ways.
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