Answer:
y = 4x - 8
Step-by-step explanation:
x = 1/4y + 2
-1/4y -1/4y
-1/4y + x = 2
-x -x
-1/4y= -x + 2
*-4 *-4
y = 4x - 8
Hey!
------------------------------------------------
Solution:
~Subtract x to both sides
x - x = 1/4y + 2 + (-x)
~Simplify
1/4y = 2 + (-x)
~Multiply 4 to both sides
1/4y * 4 = 2 + (-x) * 4
~Simplify
y = 8 - 4x
~Switch
y = 4x - 8
------------------------------------------------
Answer:
[tex]\large\boxed{y~=~4x~-~8}[/tex]
------------------------------------------------
Hope This Helped! Good Luck!
If G={(-1,7),(8,2),(0,0),(6,6)}, then the range of G is
Answer: [tex]Range:\{0,2,6,7\}[/tex]
Step-by-step explanation:
By definition:
1) The Domain is the the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
2)the Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair).
In this case you have the following relation "G":
[tex]G=\{(-1,7),(8,2),(0,0),(6,6)\}[/tex]
Based on the definition shown before, you can conclude that the Domain of G is:
[tex]Domain: \{-1,0,6,8\}[/tex]
And the Range of G is the following:
[tex]Range:\{0,2,6,7\}[/tex]
What is the value of x that makes the given equation true? 2(x−8)=x+5x
Answer:
x = - 4
Step-by-step explanation:
Given
2(x - 8) = x + 5x ← distribute left side and simplify right side
2x - 16 = 6x ( subtract 6x from both sides )
- 4x - 16 = 0 ( add 16 to both sides )
- 4x = 16 ( divide both sides by - 4 )
x = - 4
A principal evenly distributes 6 reams of copy paper to 8 fifth-grade teachers.
a. How many reams of paper does each fifth-grade teacher receive? Explain how you know using pictures, words, or numbers.
b. If there were twice as many reams of paper and half as many teachers, how would the amount each teacher receives change? Explain how you know using pictures, words, or numbers.
Answer: We start with 6 reams of copy paper and 8 teachers.
a) if we distribute the paper equally between all the teachers, then each teacher receive 6/8 (here we are dividing the total number of reams by the number of people that we are are splitting it). but 6/8 is less than one, so we must open the reams in order to split them.
b) If there were twice as many reams of paper, then we will have 2*6 = 12 reams of paper, and if there where half the number of teachers, then we have 8/2 = 4 teachers.
Doing the same procedure as before, we have 12 teams for 4 teachers, then each teacher has 12/4 = 3 reams
before, each teacher received 6/8 reams, and now, each one receive 3.
if we want to know the change, we need to see the difference between these numbers, so 3 - 6/8 = 3*8/8 - 6/8
notice that i am multiplying the 3 by 8/8, this is one, but this way i can have the same denominator in both numbers.
24/8 - 6/8 = 18/8 = 9/4 = 8/4 + 1/4 = 2 + 1/4
so each teacher receive 2 + 1/4 reams than before.
Use the graph shown to fill in the blank.
When x = -3, then y = a0.
Answer: -6
Step-by-step explanation:
When X = - 3, then Y = -6
Slope is 2.
Answer:
When x = -3, then y = -6
Step-by-step explanation:
We need to find out the value of y when x=-3
From the graph we look at the value of y
x is the input of the graph and y is the output .
In x axis the positive numbers on the right side and negative numbers on the left side . In y axis the positive numbers at the top and negative numbers at the bottom.
Given x=-3, Lets find the value of
At x=-3 the graph is at the bottom of x axis
Draw a line down at x=-3 , the line meets the graph at -6
So at x=-3 the value of y is -6
When x = -3, then y = -6
4. At 840,000 square miles, Greenland is the largest island
in the world. The second-largest island is
New Guinea, at 306,000 square miles. How much large
is Greenland than New Guinea?
Answer:
840,000 / 306,000 = 2.7450980392
So, Greenland is about 2 and 3/4 times larger than New Guinea.
Step-by-step explanation:
Greenland, the largest island in the world, is 534,000 square miles larger than New Guinea.
Explanation:Greenland is 840,000 square miles and New Guinea is 306,000 square miles. To find out how much larger Greenland is than New Guinea, we subtract the area of New Guinea from the area of Greenland:
840,000 - 306,000 = 534,000 square miles
Therefore, Greenland is 534,000 square miles larger than New Guinea.
To determine how much larger Greenland is than New Guinea, one must subtract the size of New Guinea from the size of Greenland. Given that Greenland, the largest island in the world, is 840,000 square miles and New Guinea is 306,000 square miles, you would perform the following calculation:
840,000 - 306,000 = 534,000 square miles
Therefore, Greenland is 534,000 square miles larger than New Guinea.
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Mary has 12 hair ribbons. 3 of the ribbons are red. What percent of her ribbons are red?
Answer:36%
Step-by-step explanation:
Answer:
25%
Step-by-step explanation:
3 ribbons/ 12ribbons= 1/12
If You simplify dividing by 3 it becomes =1/4 = 0.25
so.. this is the 25 %
Faye has 5 pieces of ribbon, each 1 yard long. She cuts each ribbon into sixths.
a. How many sixths will she have after cutting all the ribbons?
b. How long will each of the sixths be in inches?
Answer:
a ) total number of sixth in 5 ribbon will be 6\times 5 = 30
b) length of each sixth will be = 5.97 inches
Step-by-step explanation:
given data:
Number of pieces of ribbon is 5
each piece length 1 yard
total number of cut in one piece of ribbon = 6
a) one piece of ribbon consist of 6 sxiths
therefore total number of sixth in 5 ribbon will be 6\times 5 = 30
b) each ribbon length is 1 yard
so, whole ribbon is divided into 1\6 yard length which is length of individual division
we know that one yard is 36 inches
therefore, in 1/6 yard = 5.97 inches
Answer:
a. She will have 30 sixths after cutting all the ribbons.
b. 6 inches.
Step-by-step explanation:
a. You know that the lenght of each piece of ribbon is 1 yard.
She cuts each ribbon into sixths, then the lenght of each one of them is:
[tex]\frac{1}{6}\ yd[/tex]
So:
[tex]\frac{6}{6}=1\ yard[/tex]
Since Faye has 5 pieces of ribbon, after cutting all the ribbons she will have:
[tex](5)(\frac{6}{6})=\frac{30}{6}[/tex]
She will have 30 sixths after cutting all the ribbons.
b. You need make the conversion from yards to inches.
Knowing that [tex]1\ yd=36\ in[/tex], you get:
[tex](\frac{1}{6}\ yd)(\frac{36\ in}{1\ yd})=6\ in[/tex]
which of the following values are in the range of the function graphed below? check all that apply
Answer:
Option D. 1
Option E. 1/2
Step-by-step explanation:
we know that
Looking at the graph
The domain is the interval ----> [-1,1]
[tex]-1\leq x\leq 1[/tex]
The domain is all real numbers greater than or equal to -1 and less than or equal to 1
The range is the interval ----> [0,1]
[tex]0\leq y\leq 1[/tex]
The range is all real numbers greater than or equal to 0 and less than or equal to 1
therefore
The values that are in the range are
1 and 1/2
Answer:
D.1
E.[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We have to find the values lie in the range of function in given graph.
Let f(x) be given function
Domain takes along x- axis and range takes along y- axis.
From given graph , we can see that
Domain of function =[-1,1]
It means
[tex]-1\leq x\leq 1[/tex]
Range of function:[0,1]
It means
[tex]0\leq y \leq 1[/tex]
The value of range of given function from 0 to 1.
Hence, option D and E are correct.
D.1
E.[tex]\frac{1}{2}[/tex]
What is the true solution to the equation below?
In elnx+ In enx=-2 In 8
To solve the given equation, w need to review some rules:
The given equation is :
⇒⇒⇒⇒ rule (2)
⇒⇒⇒⇒ rule (1) and rule (2)
⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides
∴ x = 4
So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4
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The solution of the logarithmic equation is x = 4
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
[tex]ln[e^{ln ( x )} ] + ln[e^{ln (x^{2} )} ] = 2ln(8)[/tex]
On simplifying , we get
The value of ln e = 1
From the laws of logarithm , we get log Aⁿ = n log A
ln ( x ) ln ( e ) + ln ( x )² ln ( e ) = 2 ln ( 8 )
On further simplification , we get
ln ( x ) + ln ( x )² = ln ( 8 )²
From the laws of logarithm , we get log A + log B = log AB
ln ( x )³ = ln ( 64 )
ln ( x )³ = ln ( 4 )³
So , the value of x = 4
Hence , the logarithmic equation is solved
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find the decimal that is equivalent to 7/12
Answer: 0.58333333333333
Step-by-step explanation: To find the decimal that is equivalent to 7/12, remember that fractions are division problems so we can divide the numerator by the denominator.
Numerator = 7
Denominator = 12
7 ÷ 12 = 0.58333333333333.
Answer:
_
.583
Step-by-step explanation:
In order to convert 7/12 to a decimal you must divide 7/12. The answer won't be a rational number, but will be a repeating decimal. You end up with .583 with 3 repeating. To show that this is repeating, you must put a little bar over the 3 (Because the 3 is the only repeating number) like so:
_
.583
I hope I was helpful!
Which equation has solutions of 6 and -6?
Answer:
x^2-36=0
Step-by-step explanation:
x^2-36=0
(x-6)(x+6)
Answer:
[tex]x^2-36=0[/tex]
Step-by-step explanation:
Solution is 6 and -6. Lets check with each option
[tex]x^2-12x+36=0[/tex]
[tex](x-6)(x-6)=0[/tex]
x-6=0 so x=6
Solutions are 6 and 6. First option does not gives us solution 6 and -6
[tex]x^2+12x-36=0[/tex]. It is not factorable
[tex]x^2+36=0[/tex]. It is not factorable
[tex]x^2-36=0[/tex]
[tex](x+6)(x-6)=0[/tex]
x-6=0 , so x=6
x+6=0, so x=-6
[tex]x^2-36=0[/tex] is the final answer
5b + 2= 17 two step equation
Answer: 5b = 15
Step-by-step explanation:
5b + 2 = 17
- 2 -2
5b = 15
The two steps are:
step 1 : 5b = 17 - 2
step 2 : b = 15/5
Given,
5b + 2= 17
Now,
The equation given two us is in linear form with one variable .
So,
Simplifying the equation,
5b + 2= 17
Take 2 from LHS to RHS
5b = 17 - 2
5b = 15
b = 15/5
b = 3
Thus the value of b is 3 .
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In the diagram below angle AED=(4n-20)° and angle BEC=(2n-16)°. What is the measure of angle CED in degrees
(See picture)!!
Check the picture below.
so, bearing in mind that vertical angles are equal, thus ∡AED = ∡BEC, and we know that ∡BEC = 52 = ∡AED, so those two angles added up are 104°.
now, a circle has a total of 360°, if we take away those 104° from the red angles, what's leftover is just 256°, well, the green angles there are also vertical angles and thus twins, so each one will take half of 256°.
∡BEA = 128° = ∡CED.
The length of a rectangle is 15 and its width is w.
The perimeter of the rectangle is, at most, 50,
Which inequality can be used to find the longes
possible width?
A
30+ 2x < 50
B. 30 + 2w < 50
D. 30+ 2w > 50
C.30 + 2w > 50
A rectangle with sides 15 and w has perimeter
[tex]2p = 2(15+w) = 2w+30[/tex]
We want this quantity to be at most 50, so it must be less than or equal to 50:
[tex]2w+30\leq 50[/tex]
For the record, this implies that
[tex]2w\leq 20 \iff w \leq 10[/tex]
So, the width can be at most 10.
Answer:
2x+30< 50 ...answer : A
Step-by-step explanation:
the perimeter is : P = 2(L+W)
let : L= x given : L=15
P= 2(x+15)
The perimeter of the rectangle is, at most, 50: P<50
2(x+15) < 50
2x+30< 50 ...answer : A
Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Which of the following are true? Select all that apply.
A. One pound of pistachios plus 1 pound of almonds cost $20.
B. The pistachios cost twice as much per pound as the almonds.
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
D. The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Answer:
A. One pound of pistachios plus 1 pound of almonds cost $20
C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.
E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.
Step-by-step explanation:
Let
x ----> the cost of one pound pistachios
y ----> the cost of one pound of almonds
we know that
x=y+4 -----> equation A
2x+3y=48 -----> equation B
substitute equation A in equation B and solve for y
2(y+4)+3y=48
2y+8+3y=48
5y=48-8
y=8
Find the value of x
x=8+4 =12
therefore
The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8
Verify all statements
case A) One pound of pistachios plus 1 pound of almonds cost $20.
Is True
x+y=$12+$8=$20
case B) The pistachios cost twice as much per pound as the almonds
Is false
Because
2y=2(8)=$16
$16≠$12
case C) Reducing the number of pounds of almonds by 1 results in a total cost of $40
Is True
Because
2x+2y=2(12)+2(8)=$40
case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.
Is false
The equation will be
2(a + 4) + 3a = 48.
case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48
Is true
Because
p=a+4
Solve for a
a=p-4
When rounding to the nearest hundred, what is the least whole number that rounds to 900?
Answer:
850 rounds up to 900
Step-by-step explanation:
if it's 5 or more it will go up, if it were 840 it'll drop to 800
Sam bought one dozen eggs from the grocery store to bake some cakes.how many eggs did Sam buy?
Answer:
He buy 12 eggs from grocery.
Because,
1 dozen of a thing(x) = 12 things(x)
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Find y if the line through (3,5) and (6,y) has a slope of 2
Answer:
The answer is y = 11.
Help me with answer 9
Answer:
64
Step-by-step explanation:
2 to the power of 3 is 8 and 2 to the power of 4 is 16 and 2 to the power of 1 is 2 and 16 divided by 2 is 8 and 8 times 8 equals 64
write three numbers that have GCF of 7
Answer:
21, 35 , 49
Step-by-step explanation:
21 = 3 * 7
35 = 5 * 7
49 = 7 * 7
GCF = 7
in an isosceles triangle if a base angle has a measure of 55 degrees then the vertex angle must have a measure of 70 degrees as well
Answer:
True
Step-by-step explanation:
The base angles of an isosceles triangle are equal.
The sum of the 3 angles in a triangle = 180°, thus
vertex angle = 180° - (55 + 55)° = 180° - 110° = 70°
Jeremiah and Cynthia each run a lemonade stand. They decide that they will share the
money they make evenly Jeremiah makes $237 at his stand and Cynthia makes $218.
After they combine and split up their money evenly, which statement must be true
a. They each get $229 with no money left over
b. They each get $228 with $1 left over
C. They each get $910 with no money left over
d. It is not possible to share their money evenly
Answer:
I believe it's D.
Step-by-step explanation:
if you add 237 + 228 you get 455. 455 divide by 2 is 227.5 which doesn't make it even.
Is 21/32 greater than 3/4
Answer:
Step-by-step explanation:
It's highly advisable to find and use the LCD in problems like this.
21/32 has the denominator 32; if we multiply numerator and denominator each of 3/4, we get the equivalent fraction 24/32.
Now, compare 21/32 and 24/32. It's pretty obvious that "21/32 greater than 3/4" is false; 24/32 is greater than 21/32, so 3/4 is greater than 21/32.
∡rst is a right angle. if rs has a slope of 3, what must be the slope of st?
Answer:
The slope of st is -1/3
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m1*m2=-1[/tex]
we have
[tex]m1=3[/tex]
substitute and solve for m2
[tex](3)*m2=-1[/tex]
[tex]m2=-\frac{1}{3}[/tex]
therefore
The slope of st is -1/3
rearrange the formula to make a) f the subject and b) v the subject. 1/v+1/u=1/f
Answer:
see explanation
Step-by-step explanation:
Multiply through by the lowest common multiple of u, v and f, that is uvf
uvf × [tex]\frac{1}{v}[/tex] + uvf × [tex]\frac{1}{u}[/tex] = uvf × [tex]\frac{1}{f}[/tex], that is
uf + vf = uv ← factor out f on the left side → (1)
f(u + v) = uv ← divide both sides by (u + v)
f = [tex]\frac{uv}{u+v}[/tex]
(b)
Using line (1)
uf + vf = uv ( subtract uv from both sides )
uf + vf - uv = 0 ( subtract uf from both sides )
vf - uv = - uf ← factor out v on the left side
v(f - u) = - uf ← divide both sides by (f - u)
v = - [tex]\frac{uf}{f-u}[/tex]
If y represents a number, then write an expression for negative two times the sum of y and 7
The required expression would be -2(y+7) represents which is negative two times the sum of y and 7.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?
Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have been given that y represents a number.
To determine the expression for negative two times the sum of y and 7.
As per the given statement,
So the expression would be -2(y+7).
Hence, the required expression would be -2(y+7) represents which is negative two times the sum of y and 7.
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Subtract 582,295 from670,63
Answer: 100,335
Step-by-step explanation: Whenever you see the terms "subtract _____ from blank," the numbers in the equation will be reverse. For example, subtract 76 from 100 would be translated as 100-76. This applies here. The equation is 670,630-582,295, which is 100,335
HELP ASAP ILL GIVE U BRAINLEST
Answer:
the answer is A
Step-by-step explanation:
Answer:
(-1,5)
Step-by-step explanation:
(?,0)
(-1,0)
(5,0)
Michael saves $423 dollars a month for college.
a. About how much money will he have saved after 4 years?
b. Will your estimate be lower or higher than the actual amount Michael will save? How do you know?
Answer:
(a). $20,000
(b). The estimate will be lower than the actual amount.
Step-by-step explanation:
We have been given that Michael saves $423 dollars a month for college.
(a). We know that 1 year equals 12 months.
4 years = 4*12 months = 48 months.
[tex]\text{Actual amount saved}=\$423\times 48[/tex]
Since we are asked to find the estimated amount of money Michael will save in 4 years, so we will estimate both quantities as:
[tex]423\approx 400\\\\48\approx 50[/tex]
[tex]\text{Actual amount saved}=\$400\times 50[/tex]
[tex]\text{Actual amount saved}=\$20,000[/tex]
Therefore, Michael will save approximately $20,000 in 4 years.
(b).
The estimate will be lower than the actual amount as we rounded $423 down $23 to nearest hundred that is $400 and rounded 48 up 2 to nearest ten that is 40.
Therefore, the estimate will be lower than the actual amount.
is (-2,-1) , (1,-4) and (5,-3) , (-2,-8) perpendicular?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's find the slopes of these two, if they're indeed perpendicular, they'll be negative reciprocal of each other, meaning one slope will be the same as the other, but negative and upside-down, and thus their product will just be -1.
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-2)}}}\implies \cfrac{-4+1}{1+2}\implies \cfrac{-3}{3}\implies \boxed{-1} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-8+3}{-7}\implies \cfrac{-5}{-7}\implies \boxed{\cfrac{5}{7}}[/tex]
well, 5/7 is not the negative reciprocal of -1.