The value of x is 1 and -8.
To solve this problem we need to understand the concept of quadratic equation.
To solve Quadratic equation we need to understand the concept of equation which says the factor of the product of coefficient of [tex]x^{2}[/tex] and constant must on adding or substracting give the coefficient of x.
Here the equation is [tex]x^{2} +7x-8=0[/tex]
The product of coefficient is 8. The factors of 8 is 8 and 1 which gives 7 on substracting.
Now,
[tex]x^{2} +8x-x-8=0[/tex]
⇒[tex]x(x+8)-1(x+8)=0\\[/tex]
⇒[tex](x-1)(x+8)=0[/tex]
∴ x=1,-8.
So, the required values of x is 1 and -8.
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1=|8-2y| what’s the value of y
Answer:
y=-7/2
Step-by-step explanation:
1=|8-2y|
1=8+2y
-7=2y
2y=-7
y=-7/2
版 < The population of a village 10 years ago was 7500. The population is now 5700. What percentage decrease is this? Type here to search O 21 7 I %
Four thousand five hundred eleven ten-thousandths in standard decimal form?
Find the slope of the line shown on the graph to the right.
Question content area bottom left
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
The slope would be [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Answer:
-4/-5
Step-by-step explanation:
Remember the formula to slope:
(y2 - y1)/(x2-x1) given two points on the line that are (x1, y1) and (x2, y2).
The two points given on this line are: (2,2) from the top left and (-3,-2) from the bottom left. Let's say (2,2) = (x1, y1) and (-3,-2) = (x2, y2). Plug the points into the formula:
(-2 - 2)/(-3-2) = -4/-5
FINAL ANSWER: -4/-5
A car company uses the table below to show customers the approximate amount of gas used when a car has been driven a certain number of miles.
Gas Use
Miles driven
Gallons of gasoline used
120
6
300
15
360
18
480
?
If the car always uses the same amount of gasoline each mile, how many gallons of gasoline would be needed to travel 480 miles?
A.20
B.24
C.33
D.39
The diameter, D, of a sphere is 9.4 m. Calculate the sphere's volume, V.
Use the value 3.14 for , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
V = m^3
Answer: v=M^3
Step-by-step explanation:
Points A and B are plotted on a number line at -4 and 3. respectively. Find the coordinate of the point that represents the weighted averag
of A and B if point A has a weight of 2 and point B has a weight of 5.
The coordinate of the pointed that represented the weighted average of A and B is: 1
What is the explanation for the above?Note that X = [x1w1 + x2w2 +.......xnwn]/w1+w2 +....wn
Where x is the numbers and w is the weight.
Given,
A = - 4 : Weight = 2
B= 3 : Weight = 5
Hence, average is given as;
([-4 x 2] + [3 x 5])/2+5
= (-8 + 15)/7
= 7/7
= 1
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I need help on question 82 a,b,c,d,e
Answer:642
Step-by-step explanation:
Look at the book and solve it
If z/4+3=-2 what is the value of z/4+7?
Put your answer in the form of [x]
Answer: x=2
Step-by-step explanation:
x=z/4+7
x=z/4+3+4
x=(z/4+3)+4
x=-2+4
x=2
Write the linear function y that has the given function values.
f(−6) = −7, f(1) = 2
The equation of this linear equation is f(x) = 9/7(x - 1) + 2
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the linear equation?The given parameters are
f(−6) = −7, f(1) = 2
Start by calculating the slope (m) using
m = [f(-6) -f(1)]/[-6 - 1]
This gives
m = [-7 - 2]/[-6 - 1]
Evaluate
m = 9/7
The linear equation is then calculated as
f(x) = m(x - x1) + f(1)
So, we have
f(x) = 9/7(x - 1) + 2
Hence, the equation of this linear equation is f(x) = 9/7(x - 1) + 2
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Find a + b, 9a + 3b, |a|, and |a − b|. a = 9i − 4j + 3k, b = 6i − 9k
1) a + b = ?
→ (9i − 4j + 3k) + (6i − 9k)
→ 15i - 4j - 6k
2) 9a + 3b = ?
→ 9(9i − 4j + 3k) + 3(6i − 9k)
→ (81i - 36j + 27k) + (18i - 27k)
→ 99i - 36j
3) |a| = ?
→ |9i − 4j + 3k|
→ 9i + 4j + 3k
4) |a − b| = ?
→ |(9i − 4j + 3k) - (6i − 9k)|
→ |3i - 4j + 12k|
→ 3i + 4j + 12k
Answer:
[tex]a+b=15i-4j-6k[/tex]
[tex]9a+3b=99i-36j[/tex]
[tex]|a| = 9i+4j+3k[/tex]
[tex]|a-b| = 3i+4j+12k[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]
[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]
[tex]\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}[/tex]
[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]
[tex]\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}[/tex]
Let U= {x | x is a whole number and 0 ≤ x ≤ 19) and C= {15, 16, 17, 18, 19). Write U U C using the listing method.
UUC=
set, in mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.
Let C=15, 16, 17, 18, and 19) and U=x | x is a full number and 0 x 19). Use the listing technique to write U U C.
UUC=
D U E = { 16, 18, 19, 20, 21 }
U stands for the union of sets.
We combine all of the components from the two groups.
16, 19, 21, and 16, 18, 19, 20 are the elements in sets D and E, respectively.
Therefore, we combine all of their components. The shared components of both sets are written just once.
As a result, there are 16, 18, 19, 20, and 21 elements in the set D U E.
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|3x| = 11.4 absolute value of X
Step-by-step explanation:
The absolute value of x is g(x)=f(x)+k.
If 3 times a number is decreased by 2 the principal square root of this difference is 4 less than the number. Find the number(s).
The numbers are -3 and 6
How to determine the numberFrom the information given, let the number be x;
the expression is given as;
(√3x + 2) = x - 4
To determine the number, find the square of both sides, we have;
(√3x + 2) ^2 = (x - 4)^2
Find the square of both sides
3x + 2 = ( x - 4)(x + 4); difference of two squares
expand the bracket
3x + 2 = x^2 + 4x - 4x - 16
collect like terms
x^2 - 3x - 16 - 2
x^2 - 3x - 18
x^2 - 6x + 3x - 18
Factorize the expression
x( x - 6) + 3( x - 6)
(x + 3) or (x - 6)
x = -3 or x = 6
Thus, the numbers are -3 and 6
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A square that is 7 yd on a side is placed inside a rectangle that has a width of 9 yd and a length of 14 yd. What is the area of the region inside the rectangle that surrounds the square?
Answer: 77 yd^2
Step-by-step explanation:
S=Area of Square. s=side length of square. w=width of rectangle
l=length of rectangle. R=Area of Rectangle
S=s^2
S=7^2
S=49 yd^2
R=l*w
R=9*14
R=126 yd^2
R-S=
126-49=77 yd^2
i need help with this assignment can anyone help
Answer: 18.25
Step-by-step explanation:
5.5*4=22
401.5/22=18.25
Answer:
$18.25
Step-by-step explanation:
Since area is given as A=LW, and we are given the values of the dimensions of the floor, we get:
5.5×4=22
So, the area is 22 yards, and it costs $401.5 to carpet it. Now, We simply need to divide the cost by the area to get the "cost per-square yard" as needed in the question. We get:
401÷22=18.25
So, the cost of the carpet per square yard is $18.25
Tim always eats strawberries in multiples of three. Todd eats them in multiples of four and Rick in multiples of six. Gavin is not fussy
about it but likes cream to go with them. Uncle Sam wants each of the four kids to eat the same number of strawberries. What is the
minimum number of strawberries that he has to give to each kid?
Answer:
12
Step-by-step explanation:
3*4 = 12
12/6 = whole number
6/4 is not a whole number
12 is the lowest it could be.
Also those kids have issues.
A 5.ft tall man casts a shadow along the ground that is 8 ft. long. At the same time a giraffe casts a shadow that is 12 ft. long. How tall is the Giraffe?
Answer : 7.5 ft
Step-by-step explanation:
when the length of the shadow is 8ft, the actual height of the man = 5ft
8:5
let the giraffe be 'x' ft tall.
if the length of the shadow is 12ft, actual height = x ft
12:x
8:5 x 12:x
[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]
x= [tex]\frac{15}{2}[/tex]
x=7.5 ft
Therefore, the giraffe is 7.5ft tall.
Answer:
[tex]7.5\; {\rm ft}[/tex].
Step-by-step explanation:
The height of objects nearby under the sun are approximately proportional to the length of their shadows.
In other words, if the man and the giraffe are near each other and under the sun:
[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].
Given that:
[tex](\text{height of man}) = 5\;{\rm ft}[/tex], [tex](\text{length of shadow of man}) = 8\;{\rm ft}[/tex], and [tex](\text{length of shadow of giraffe}) = 12\; {\rm ft}[/tex].Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:
[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].
this week Jada bought a 3 1/2 pound of cat food. her cat eats 5/8 of a pound each day. show your work and remember to include units. check your work with multiplication
Answer:
5 days.
Step-by-step explanation:
The food will last her 5 days.
[tex]3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1-\frac{5}{8}[/tex][tex]=\frac{3}{8}[/tex]
Which expression is equivalent to (a2/3 1/31/22
OA 7/665/6
OB. 44/32/3
Oca1/261/2
C.
OD. a4/361/6
OE.al/361/6
Answer:
E. a^(1/3)b^(1/6)
Step-by-step explanation:
You want an expression equivalent to (a^(2/3)b^(1/3))^(1/2).
Rules of exponentsThe applicable rules of exponents are ...
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
ApplicationThe given expression simplifies to ...
[tex](a^{2/3}b^{1/3})^{1/2}=a^{(2/3)(1/2)}b^{(1/3)(1/2)}=\boxed{a^{1/3}b^{1/6}}[/tex]
If an individual makes $4,000 in salary per month and has a side job making $20 per hour for 10 hours a week for 4 weeks in a
month, and they receive $1,000 per month in rent from a roommate, what is their gross income?
O $4,000
O $4,800
O $5,800
O Cannot be determined, because taxes and deductions are not provided
The gross income will be $5,800.
It is given that per month salary of an individual is $4000 and from a side job he makes $20 per hour for 10 hours a week for 4 weeks and rent he got is $1000.
We have to calculate the gross income.
What do you mean by gross income ?
Gross income refers to the total income of a person or business from all resources.
As per the question ;
Per month salary = $4000
Earning from side job is given $20 per hour for 10 hours a week for 4 weeks.
i.e.,
= 20 × 10 × 4
= $800 for 4 week
and
the rent they receive = $1000
So ;
The gross income will be ;
= 4000 + 800 + 1000
= $5,800
Thus , the gross income will be $5,800.
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Please help simplify
Answer: B. 24
Step-by-step explanation:
A number, x, rounded to 1 decimal place is 12.3
Write down the error interval for x.
The error of interval for x will be [12.25, 12.35) for rounding off to 12.3 to 1 decimal place
In the given question, a number supposed to be 'x' is rounded off to the 1 decimal place, so that the number rounded off becomes 12.3. So, it is given that the number x is rounded off to 12.3 by 1 decimal place.
From this, we get that x should be greater than or equal to 12.25 and x should be smaller than 12.35. The equations will be :
=> x ≥ 12.25 and x < 12.35
So, the x lies between 12.25 and 12.35 which defines the error of interval for x.
Hence, the error of interval for x will be [12.25, 12.35)
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Question
Your bank account has a balance of −$12. You deposit $60. What is your new balance?
Your new balance is $
.
Answer: $52 is your new balance
Step-by-step explanation: -12+60=52
A rectangular picture has dimensions of length (2x-1) inches and width (x+7) inches. The area of the picture is 108 in^2. What are the length and width of the picture?
The numerical length and width of the rectangular picture are 9in and 12in respectively.
What are the length and width of the picture?Area of a rectangle is expressed as;
A = length × width
Given the data in the question;
Length = 2x -1Width = x + 7Area = 108in²To determine the numerical length and width of the rectangular picture, first plug the given values into the equation and solve for x.
A = length × width
108 = (2x -1)(x+7)
Expand
108 = 2x² + 14x - 1x -7
108 = 2x² + 13x -7
Reorder
2x² + 13x -7 = 108
2x² + 13x - 7 - 108 = 0
2x² + 13x - 115 = 0
Solve by grouping
(x-5)(2x+23) = 0
x-5 = 0, 2x+23 = 0
x = 5, 2x = -23
x = 5, x = -23/2
x = 5, x = -11.5
But the dimension cannot be negative, hence;
x = 5
Next, determine the numerical length and width.
Length = 2x - 1 = 2(5) - 1 = 10 - 1 = 9in
Width = x + 7 = 5 + 7 = 12in
Therefore, the numerical length and width of the rectangular picture are 9in and 12in respectively.
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Please refer to the picture, thank you!!!
An equation that relates T to N can be written as T = 750 + 630N.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
What is a function?A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).
How to write an equation relating T to N.Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:
T = A + B
Substituting the given parameters into the formula, we have;
T = (750 + 135N) + 495N
T = 750 + 135N + 495N
T = 750 + 630N.
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Complete Question:
Raina and her husband are each starting a saving plan. Deshaun will initially set aside $750 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+135N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $495 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=495N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.
Simplify your answer as much as possible.
pedro wants to make 3 1/2 batches of granola bars. His dad tells him that he needs 5 1/4 cup of oatmeal. How much oatmeal does pedro need for a single batch
Pedro requires [tex]1\frac{1}{2}[/tex] cups oatmeal for a single batch of granola bars as calculated by division of fractions.
A fraction is a piece of a whole or, to put it more broadly, any number of equal portions.
The Latin word fractus, which means "broken," is where the word fraction originates.A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of components of a particular size as it is represented in common English. There is a non-zero denominator and a common, or simple fraction below (or after) that line.Compound fractions, mixed numeral fractions, and difficult fractions are examples of uncommon fractions that use numerators and denominators.Total batches required [tex]= 3 \frac{1}{2} = \frac{7}{2} = \frac{14}{4}[/tex] cups
Total oatmeal required [tex]= 5 \frac{1}{4} =\frac{21}{4}[/tex] cups
Therefore now to calculate the amount of oatmeal needed for single
batch we divide the fraction [tex]\frac{21}{4}[/tex] by [tex]\frac{14}{4}[/tex] cups
1 batch requires = [tex]=\frac{21}{4}\div\frac{14}{4}=\frac{3}{2} = 1\frac{1}{2}[/tex] cups.
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What numbers are a distance of 34 unit from 18 on a number line?
Select the locations on the number line to plot the points.
Answer:
[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]
Step-by-step explanation:
To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]
One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away
Compute [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4} :[/tex]Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width.
Set up your solution using the variables L for the length, W for the width, and P for the perimeter.
Part a: Using the definition of perimeter, write an equation for P in terms of L and W .
Part b: Using the relationship given in the problem statement, write an equation for L in terms of W .
Solve the equations from parts a and b.
Answer:
The length should equal 27.
The width should equal 13.
A: P= 2L+ 2W
B: L=2W+1
Step-by-step explanation:
Perimeter is always equal to all of the sides added up.
You can find out the width and length by subsititution.
80=2(2W+1) +2W
80=4W+2+2W
80=6W+2
78=6W
W=13
L=(13*2)+1
L=27
PLEASE HELP I DONT UNDERSTAND
According to the image, the figure moved four times to return to its initial position.
What is the initial position of the figure?The starting position of the figure is in the lower left corner of the frame.
How does it move from position 1 to position 2?The movement made by the figure from position 1 to position 2 is that it moves from the lower left corner to the lower right corner.
How do you move from position 2 to position 3?The movement made by the figure from position 2 to position 3 is that it moves from the lower right corner to the upper right corner. Additionally, the figure rotates to the left 180°.
How does it move from position 3 to position 4?The movement that the figure performs from position 3 to position 4 is that it moves from the upper right corner to the upper left corner.
How does it move from position 4 to position 5?The movement made by the figure from position 4 to position 5 is that it moves from the upper left corner to the lower left corner. Additionally, the figure is rotated 180° to the left again.
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