Multiply. Express your answer in simplest form. 5/8 x 4/7
Answer 5/14
Step-by-step explanation:
The simplest form of the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] is [tex]\frac{5}{14}[/tex].
An expression is a combination of numbers, variables, operations, functions, and often symbols that are combined according to particular rules to represent a mathematical computation or relation.
Expressions can be both simple as a single number or variable and complex by involving multiple variables and operations.
Some examples of Expressions are x, 4, x² + 6y + 2xy +6, [tex]\frac{x}{y}[/tex], [tex]\frac{x}{y} \times \frac{p}{q} \div e^7[/tex] etcectra.
The given expression is
[tex]\frac{5}{8} \times \frac{4}{7}[/tex] [tex]= \frac{5}{2}\times \frac{1}{7}[/tex]
[tex]= \frac{5\times1}{2\times7}\\ = \frac{5}{14}[/tex].
Hence the given expression [tex]\frac{5}{8} \times \frac{4}{7}[/tex] can be simplified as [tex]\frac{5}{14}[/tex].
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Which of the following points are solutions to the equation
y=3x+5
(7,16)
(-2,1)
(2,11)
(-7,16)
select two
I only get one (2, 11)
to find the points which are solutions, substitute the x-coordinate into the equation and if the value obtained equals the y-coordinate of the point then it is a solution
(7, 16) : y = (3 × 7 ) + 5 = 21 + 5 = 26 ≠ 16
( - 2, 1): y = (3 × - 2) + 5 = - 6 + 5 = - 1 ≠ 1
(2, 11) : y = (2 × 3) + 5 = 6 + 5 = 11
( - 7,16 ): y = (3 × - 7) + 5 = - 21 + 5 = - 16 ≠ 16
the only point from the given list that is a solution is (2 , 11)
By substituting the x and y values of the given points into the equation 'y = 3x + 5', we can determine that the only solution from the given points is (2,11).
Explanation:The given equation is y = 3x + 5. We can find out which of the points are solutions to the equation by substituting the x-coordinate and y-coordinate of each point into the equation. If the equation holds true, then the point is a solution.
For the point (7, 16), the equation becomes 16 = 3*7 + 5. This simplifies to 16 = 21 + 5. This is not true, so (7, 16) is not a solution. For the point (-2,1), the equation becomes 1 = 3*(-2) + 5. This simplifies to 1 = -6 + 5. This is also not true, so (-2,1) is not a solution. For the point (2, 11), the equation becomes 11 = 3*2 + 5. This simplifies to 11 = 6 + 5, which is true, so (2,11) is a solution. For the point (-7,16), the equation becomes 16 = 3*(-7) + 5. This simplifies to 16 = -21 + 5. This is not true, so (-7,16) is not a solution.
So, the points that are solutions to the equation y = 3x + 5 are (2,11).
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Which ordered pair (m, n) is a solution to the given system of linear equations?
6m-5n= 14
2m+2n= -10
a) (-4,-1)
b) (-31/11,-24/110
c) (-1,-4)
d) (11,-16)
ANSWER: NOT B
Answer:
Option C
Step-by-step explanation:
given two equations
6m-5n= 14 ... i
2m+2n= -10 ...ii
We can solve this by elimination.
For elimination consider the coefficients of m.
They are 6 and 2, with LCD 6
You multiply 2nd equation by 3 to have
6m+6n =-30 ... iii and
6m-5n = 14 ... i
Subtract i from iii
11n = -44
Divide by 11 to get n
n = -4
Substitute in I equation
6m-5(-4) =14
6m +20 = 14
subtract 20
6m =14-20 =-6
divide by 6
m =-1
Hence answer is m=-1 and n=-4
(-1,-4)
Option C is the answer.
Factor.
12x^2-44x+7 and 35x^2-27x-18
12x^2-44x+7 = (6x - 1)(2x - 7)
35x^2-27x-18 = (7x - 9)(5x +2)
if f(x)=3x+5 and g(x)=-2x^2-5x+3, find (f+g) (x)
[tex]f(x)=3x+5,\ g(x)=-2x^2-5x+3\\\\(f+g)(x)=f(x)+g(x)=(3x+5)+(-2x^2-5x+3)\\\\=3x+5-2x^2-5x+3=-2x^2+(3x-5x)+(5+3)=-2x^2-2x+8\to\boxed{C.}[/tex]
WILL GIVE BRAINLIEST
Solve x2 + 4x − 4 = 0.
x equals the quantity of negative 2 plus or minus square root 16 all over 2
x equals negative 4 plus or minus square root 2
x equals negative 2 plus or minus 2 square root 2
x equals the quantity of 4 plus or minus square root 18 all over 2
ANSWER
[tex]x=-2\pm 2\sqrt{2}[/tex]
EXPLANATION
Given:
[tex]x^2+4x-4=0[/tex]
We complete the square as follows;
Add 4 to both sides of the equation:
[tex]x^2+4x=4[/tex]
Add half the coefficient of [tex]x[/tex] to both sides of the equation.
[tex]x^2+4x+(2)^2=4+(2)^2[/tex]
The Left Hand Side of the equation is now a perfect square.
[tex](x+2)^2=4+4[/tex]
[tex](x+2)^2=8[/tex]
Take the square root of both sides
[tex]x+2=\pm \sqrt{8}[/tex]
[tex]x=-2\pm 2\sqrt{2}[/tex]
Hence the correct answer is option C
Given equation is [tex]x^2+4x-4=0[/tex]
compare with [tex]ax^2+bx+c=0[/tex]
we get: a=1, b=4, c=-4
plug these values into quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-4 \pm \sqrt{4^2-4(1)(-4)}}{2(1)}[/tex]
[tex]x=\frac{-4 \pm \sqrt{16-4(-4)}}{2}[/tex]
[tex]x=\frac{-4 \pm \sqrt{16+16}}{2}[/tex]
[tex]x=\frac{-4 \pm \sqrt{32}}{2}[/tex]
[tex]x=\frac{-4 \pm 4\sqrt{2}}{2}[/tex]
[tex]x=-2 \pm 2\sqrt{2}[/tex]
Hence finall answer is:
[tex]x=-2+2\sqrt{2}[/tex] and [tex]x=-2-2\sqrt{2}[/tex]
Which graph represents the solution to the system of inequalities?
y ≥ x – 5
y < –x + 4
A. hope this helps. Mark as Brainliest.
Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4
Answer:
[tex]r(x)=(4x)^7[/tex]
Step-by-step explanation:
For a horizontal compression, we multiply whole numbers greater than 1 in front of [tex]x[/tex] of the given function.For horizontal expansion, we multiply by the reciprocal of the number for horizontal compression, in front of [tex]x[/tex] of the function.For example,
If we wanted to horizontally compress [tex]y=x^2[/tex], we would multiply by 4 to get [tex]y=(4x)^2[/tex], and
if we wante to horizontally expand [tex]y=x^2[/tex], we would multiply by [tex]\frac{1}{4}[/tex] to get [tex]y=(\frac{1}{4}x)^2[/tex]
Since this question asks for horizontal compression, we multiply the [tex]x[/tex] of the function by 4. So the function we need is [tex]f(x)=(4x)^7[/tex]. The second choice is correct.
barry is shopping for a new sweater that originally cost $50.00. The department store has all items marked down by 20%. He also has a coupon for an additional 10% off all purchases
Total cost of the purchase by Barry is given by the equation A = $ 36 and the amount saved by Barry is $ 14
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of all the purchase by Barry be A
Now , the equation will be
The cost of the sweater = $ 50
The marked down percentage of sweater = 20 %
So , the new cost of the sweater = cost of the sweater - ( marked down percentage x cost of the sweater )
Substituting the values in the equation , we get
The new cost of the sweater = 50 - ( 20/100 ) x 50
The new cost of the sweater = 50 - 10
The new cost of the sweater = $ 40
Now , the coupon discount percentage = 10 %
So , the final cost of the purchase A = new cost of the sweater - ( coupon discount percentage x new cost of the sweater )
Substituting the values in the equation , we get
The final cost of the purchase A = 40 - ( 10/100 ) x 40
The final cost of the purchase A = 40 - 4
The final cost of the purchase A = $ 36
So , the amount saved by Barry = cost of the sweater - final cost of the purchase
The amount saved by Barry = 50 - 36 = $ 14
Hence , the cost of the sweater is $ 36
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Simplify. Remove all perfect squares from inside the square root. 63
[tex]\sqrt{63} = \sqrt{9*7} = \sqrt{3*3*7} = 3\sqrt{7}[/tex]
The simplified form of √(63) after removing all perfect squares from inside the square root is 3√(7).
To simplify the square root of 63 and remove perfect squares, we start by finding the prime factorization of 63. The prime factorization of 63 can be obtained by dividing the number by its smallest prime factor, which is 3, and then continuing the process for each quotient until we get a prime number. The prime factorization of 63 is:
63 = 3 * 3 * 7.
Now, we look for any perfect square factors within the square root of 63. In this case, the perfect square factor is 3 * 3 (3 squared). We can remove this perfect square from the square root, leaving us with:
√(63) = √(3 * 3 * 7).
Since we removed one pair of 3's (3 * 3), the simplified square root of 63 becomes:
√(63) = 3√(7).
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What is the graph of the function?
F(x) = 1/2x^2
F(x) = 1/2x^2 is a variation of the basic graph y = x^2 (the squaring function).
The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0).
The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2). The vertex of F(x) = (1/2)x^2 is still (0,0). That eliminates the first 2 possible answers. Note that F(1) = (1/2)(1)^2 = 1/2. The point (1, 1/2) is on the third graph, but not on the fourth. Thus, the third graph is correct.
Only the third graph (option C) represents the graph of [tex]F(x) = \frac{1}{2} x^2[/tex]
The given function is:
[tex]F(x) = \frac{1}{2} x^2[/tex]
This graph is of the form [tex]y = ax^2[/tex] and it takes the shape of a parabola with center at (0, 0)
Only two of the graphs shown among the options have the center at the origin (0, 0), but only one is scaled by 0.5
Therefore, the graph of the function [tex]F(x) = \frac{1}{2} x^2[/tex] is plotted below
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What is the domain of the function y = 8x + 3/4
a) All real numbers
b) All real numbers except x = 4
c) All real numbers except x = -3/8
d) All real numbers except x = 3/8
[tex]y=\dfrac{8x+3}{4}=\dfrac{8x}{4}+\dfrac{3}{4}=2x+\dfrac{3}{4}[/tex]
It's a linear function y = mx + b. The domain of linear function is the set of all real numbers.
We have no objections to the value of x. x can be any number.
Therefore your answer is:
a) All real numbers.
5. Find the value of x. The diagram is not to scale. Lines F and G are parallel.
X=11 because
5x+9x+26=180
14x+26=180
14x=154
x=11
Answer: The required value of x is 11.
Step-by-step explanation: Given that the lines f and g are parallel to each other.
We are to find the value of x.
From the figure, we note that the parallel lines f and g are cut by a transversal, and
angles with measures 5x° and (9x+26)° are interior angles on the same side of the transversal.
We know that, if two lines are parallel, then the measures of the angles on the same side of the transversal is 180°.
Therefore, we get
[tex]5x^\circ+(9x+26)^\circ=180^\circ\\\\\Rightarrow 5x+9x+26=18\\\\\Rightarrow 14x=180-26\\\\\Rightarrow 14x=154\\\\\Rightarrow x=\dfrac{154}{14}\\\\\Rightarrow x=11.[/tex]
Thus, the required value of x is 11.
The value of zlatan's house has increased by 7%. His house is now valued at £749000 work out the value of the house before the increase
Answer:
Value of house before Increase = $700000.
Step-by-step explanation:
Let the value of house before increase be $x.
Increase in value = 7%of x= .07x
Value of house before increase+ Increase in value = Total value.
x+.07x=749000
Adding like terms,
1.07x=749000
Dividing both sides by 1.07.
x=700000.
Value of house before Increase = $700000.
In general, employment applications require all of the following except:
A.references.
B.your employment history.
C.your GPA.
D.your highest level of education.
Answer:
C.your GPA
Step-by-step explanation:
In general, employment applications require all of the following except:
C.your GPA
The GPA is not as important as the references, ones employment history and the highest level of education.
These information gives an overview about your history like if you are a fresher or an experienced person. And what education have you got, or who referred you to this particular company.
The GPA's are not considered at the first place. When a person progresses in an interview, then GPA might be considered to gather information like the person is how much efficient in that particular subject.
The length of 13 pink earasers lined up end to end is 29 1/4 inches. What would be the length of two earaser?
Jordan bought 9/16 of a pound of sunflower seeds and divided them evenly into 9 snack bags for his lunch what is the weight of sunflower seeds in each snack bag?
A)1/16 of a pound
B)1/9 of a pound
C)16/81 of a pound
D)81/16 of a pound
A.1/16 of a pound. Hope i helped
Answer:
A
Step-by-step explanation:
Ishi makes $8.50 an hour rolling sushi at kyoto japanese restaraunt his paycheck shows that he worked 20.88 hours over the past two weeks how muck did ishi earn
What is the vertex of this function f(x)=x^2+12x
Answer:
(-6, 36)
Step-by-step explanation:
The standard form: ax^2 + bx + c
In this case:
a is 1
b is 12
c is 0
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.
-12 / ( 2 x 1 )
-12 / 2
-6
You log -6 in the function
f(x) = x^2 + 12x
f(-6) = (-6)^2 + 12(-6)
= 36 + (-72)
= 36 - 72
= 36
I hope this
Answer: A (-6, -36)
Step-by-step explanation:
The question of the week! (Please show your work!)
Sarah's craft project uses pieces of yarn that are 1/8 yard long. She has a piece of yarn that is 3 yards long. How many 1/8 yard pieces can she cut and still have 1 1/4 yards left?
Rob measures his go-cart’s speed to be 250 inches per second. What is the go-cart’s speed in miles per hour (to the nearest tenth) ?
A) 7.1 mph
B) 14.2 mph
C) 28.4 mph
D) 35.2 mph
Answer:
b.14.2 mph
Step-by-step explanation:
Answer:
The cart’s speed in miles per hour is 14.2 miles per hour .
Option (B) is correct .
Step-by-step explanation:
As given
Rob measures his go-cart’s speed to be 250 inches per second.
As
[tex]1\ inch = \frac{1}{63360}\ miles[/tex]
[tex]1\ second = \frac{1}{3600}\ hours[/tex]
Now convert 250 inches per second into miles per hour .
[tex]250 inches\ per\ second = \frac{250\times \frac{1}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]
[tex]250 inches\ per\ second = \frac{\frac{250}{63360}}{\frac{1}{3600}}\ miles\ per\ hour[/tex]
[tex]250 inches\ per\ second = \frac{250\times 3600}{63360}\ miles\ per\ hour[/tex]
[tex]250 inches\ per\ second = \frac{900000}{63360}\ miles\ per\ hour[/tex]
250 inches per second = 14.2(Approx) miles per hour.
Therefore the cart’s speed in miles per hour is 14.2 miles per hour .
Option (B) is correct .
-6/5x+2=21/25 anyone?
x=-64/35
-6/5x+2= 21/25
Do fraction cross multiply
(-6*25=(5x+2)21
Then swap the sides (5x+2) *21 = (-6)*25
multiply(5x+2)21= -150/21
simplify
5x+2=- 50/7
subtact 2
5x+2-2=- 50/7-2
silmplify 5x=-64/7
divide by 5
5x/5=-64/7/5
simplify
x= -64/35
Solve:
-6/5x + 2 = 21/25
Steps:
Solution -6/5x + 2 = 21/25 =======> 29/30, Decimal =====> x = 0.96667
Subtract 2 from both sides:
-6/5x + 2 - 2 = 21/25 - 2
Simplify:
-6/5x = -29/25
Multiply both sides by -25:
(-6/5x )(-5) = (-29/25 )(-5)
Simplify:
6x = 29/5
Divide both sides by 6:
6x/6 = 29/5/6
Simplify:
Answer x = 29/30 Decimal: 0.96667....
Hope that helps!!!! : )
Zoe counts 4 times as many black kittens as white kittens for sale at the pet store. She counts a total of 25 kittens how many more black kittens does zoe count than white kittens
Answer:
Zoe counted 20 more black kittens than white kittens.
Step-by-step explanation:
Let the white kittens be = x
Then the black kittens be = 4x
Zoe counts a total of 25 kittens.
So, we get;
[tex]x+2x=25[/tex]
=> [tex]5x=25[/tex]
Dividing both sides by 5, we get;
x = 5
White kittens are = 5
Black kittens are = [tex]4\times5=20[/tex]
So, the black kittens are [tex]25-5=20[/tex] more than white ones.
Therefore, Zoe counted 20 more black kittens than white kittens.
Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4% of the total interest paid was $475 how much did he invest in each
Given
Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4%.
Total interest paid was $475
Find out he invest in each.
To proof
Let us assume that Paul invested in an account paying 4% be = x
As given in the question
Paul invested three times as much money in the account paying 5% interest then he did in an account paying 4%.
Let us assume that Paul invested in an account paying 5% be = 3x
Total interest paid = $475
First convert 4% in the decimal form
[tex]=\frac{4}{100}[/tex]
= 0.04
First convert 5% in the decimal form
[tex]=\frac{5}{100}[/tex]
= 0.05
Than the equation become in the form
0.04x + 0.05 × 3x = 475
0.04x + 0.15x = 475
0.19x = 475
x = $2500
Paul invested in an account paying 4% be = $2500
Paul invested in an account paying 5% be = $7500
Hence proved
Clara and Toby are telemarketers. Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls. If they continue at those rates, who will reach more people in 40 phone calls?
toby will reach more people in 40 phone calls
The way to solve this problem is to turn both denominators into 40
4 * 4 16
_ = --- so Clara will reach 16 people in 40 phone calls
10 * 4 40
3 * 5 15
_ = ---- so Toby will reach 15 people in 40 phone calls
8 * 5 40
Therefore Clara will reach more people in 40 phone calls than Toby.
please help on this one?
Shawn’s rectangular mobile home is 7.2 meters wide and 19.5 meters long what is the area
Answer: The area of the mobile is 140.4 m².
Step-by-step explanation:
Hi to solve this problem we have to analyze the information given:
Width : 7.2 meters (a)
Length : 19.5 meters (b)
The mobile is rectangular. So, we have to apply the area of a rectangle formula.
Area = width x length A = 7.2 x 19.5 = 140.4 m²The area of the mobile is 140.4 m².
Feel free to ask for more if it´s necessary or if you did not understand something.
Based on your knowledge of taxes you estimate the net pay will be 65%of your gross pay you think you will need 250 per week after taxes to get by. What annual gross will you need?
Answer:
You need annual gross pay of 20000.
Step-by-step explanation:
Suppose, your annual gross pay is [tex]x[/tex]
You estimate that the net pay will be 65% of your gross pay. So, the annual net pay will be: [tex]x*65\% = 0.65x[/tex]
As there are 52 weeks in 1 year, so your weekly net pay will be: [tex]\frac{0.65x}{52}[/tex]
Given that, you will need 250 per week after taxes to get by. So, the equation will be......
[tex]\frac{0.65x}{52}=250\\ \\ 0.65x= 52*250=13000\\ \\ x=\frac{13000}{0.65}=20000[/tex]
So, you need annual gross pay of 20000.
2(x+3) great her that or equal to -10 - 4x
2(x + 3) ≥ -10 - 4x
2x + 6 ≥ -10 - 4x
+4x +4x
6x + 6 ≥ -10
-6 -6
6x ≥ -16
[tex]\frac{6x}{6} \geq \frac{-16}{6}[/tex]
[tex]x \geq -\frac{8}{3}[/tex] reduced fraction
2(x+3) greater than or equal to -10 - 4x
So
2(x+3) >= -10 - 4x
2x + 6 >= -10 - 4x
2x + 4x >= -10 - 6
6x >= - 16
x >= - 16/6
x >= - 8/3
An onsite oil change service charges a flat rate of $40.00 per service call and an additional $2.25 per mile fee for travel outside a certain radius. Josh budgets $200 per year for oil changes on his vehicle. He lives 7 miles outside the radius. What is the greatest number of oil changes (c) that he can schedule and keep on budget for the year?
Answer:
c = 3 oil changes
Step-by-step explanation:
The fixed rate for oil change is $ 40
The surplus rate for miles outside the radius is $ 2.25
Josh lives 7 miles of the radius
Therefore an equation for c: The largest number of oil changes that can be scheduled and maintained within the budget for the year is:
[tex]\\40c + 2.25 * 7c = 200\\c (40 + 2.25 * 7) = 200\\c =\frac{200}{40 + 2.25 * 7}\\c = 3,578\\c = 3[/tex] oil changes
Therefore, with the budget set Josh can make a maximum of 3 oil changes per year
Answer:
The answer is 3
Step-by-step explanation
mileage fee for each oil change: 7(2.25) = $15.75
service call + mileage fee = total for each oil change
$40 + $15.75 = $55.75
c = number of oil changes
55.75c = total amount for all oil changes
55.75c ≤ 200
c ≤ 3.59
Therefore, the greatest number of oil changes that Josh can schedule without exceeding his budget is 3.