First we find how much was left as 1/8 full
16.8 times 0.125
2.1
Now add this to the amount that was added to reach full gauge
2.1 +16.8
18.9
Next we find out what 3/4 of a full tank is
18.9 times 0.75
14.175
So, the gas tank has 14.175 gallons when it is 3/4 full
the larger of two numbers is 7 less than three times the smaller number. if the sum of the numbers is 61, find the numbers
Let X = the large #
Y = the small #
We have 2 unknowns, therefore we need 2 equations to solve for them:
X + Y = 61
X = 3Y - 7
Using the substitution method we get:
X + Y = 61 original equation
(3Y - 7) + Y = 61 substituting for X
4Y - 7 = 61 combine like terms
4Y - 7 + 7 = 61 + 7 add 7 to both sides
4Y = 68 simplify
4Y/4 = 68/4 divide both sides by 4
Y = 17 solve for Y
X + Y = 61 original equation
X + 17 = 61 replace Y with 17
X + 17 - 17 = 61 - 17 subtract 17 from both sides
X = 44 solve for X
Check your answer:
X + Y = 61 X = 3Y - 7
44 + 17 = 61 44 = 3(17) - 7
61 = 61 check! 44 = 51 - 7
44 = 44 check!
Therefore, the larger #(X) = 44 and the smaller #(Y)= 17.
What is 17.318 rounded to the nearest tenth?
17.3
Because the one in the hundredths place is less than 5, so you round down to make 17.3.
-Abha
Answer: 17.3
===========================================
Explanation:
Start with the value 17.318 and note that the tenths place is just after the decimal point, so it is the 3. The digit after the 3 is 1, which is not 5 or greater. So we just drop everything after the 3 and write 17.3 as our answer
When Jose and Sean were 5 years old Jose was 1 1/2 inches taller than Sean then Jose grew at an average of 2 3/4 inches per year until he was 13 years old.jose was 63 inches tall when he was 13 years old. How tall was Sean when he was 5 years old
Sean's height when he was 5 years old is given as follows:
39.5 inches.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.Jose grew at an average of 2 3/4 inches per year, hence the slope is given as follows:
m = 2.75.
Thus:
J(x) = 2.75x + b.
Jose was 63 inches tall when he was 13 years old(8 years after he was 5 years old), hence the intercept b is given as follows:
63 = 2.75(8) + b
b = 63 - 2.75 x 8
b = 41 inches.
When Jose and Sean were 5 years old Jose was 1 1/2 inches taller than Sean, hence Sean's height is given as follows:
41 - 1.5 = 39.5 inches.
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Given that the measure of ∠x is 90°, and the measure of ∠y is 53°, find the measure of ∠z.
Final answer:
The measure of ∠z is 37°
Explanation:
To find the measure of ∠z, we can use the fact that the sum of the angles in a triangle is 180°. Thus, ∠x + ∠y + ∠z = 180°. Given that ∠x = 90° and ∠y = 53°:
90° + 53° + ∠z = 180°
Simplifying the equation:
143° + ∠z = 180°
Subtracting 143° from both sides:
∠z = 180° - 143°
∠z = 37°
The measure of angle ∠z is 37°.
The sum of the angles in any triangle is always 180 degrees. Since you've given me the measures of two angles, I can find the measure of the third angle using the following formula:
measure of angle ∠z = 180° - (measure of angle ∠x + measure of angle ∠y)
From the image, we know that:
measure of angle ∠x = 90° (given)
measure of angle ∠y = 53° (given)
Plugging these values into the formula, we get:
measure of angle ∠z = 180° - (90° + 53°)
measure of angle ∠z = 180° - 143°
measure of angle ∠z = 37°
Therefore, the measure of angle ∠z is 37°.
About how many kilometers are in 0.5 light-years?
there are 9461000000000 kilometers in a light year, aka 9.5 trillion
divide it by 2, you get 4730500000000
Simplify. 7square toot 32-6square root 72
[tex]7\sqrt{32}-6\sqrt{72}=7\sqrt{16\cdot2}-6\sqrt{36\cdot2}\\\\=7\cdot\sqrt{16}\cdot\sqrt2-6\cdot\sqrt{36}\cdot\sqrt2\\\\=7\cdot4\cdot\sqrt2-6\cdot6\cdot\sqrt2=28\sqrt2-36\sqrt2\\\\=-8\sqrt2[/tex]
[tex]Used:\\\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}[/tex]
How long will it take you to drive 315 miles at a speed of 45 miles per hour?
To find the answer you must divide both variables.
315/45 = 7
It will take 7 Hours to drive 315 Miles.
Which of the following is the correct graph of the compound inequality 4p + 1 > −11 or 6p + 3 < 39?
a number line with closed circles at negative 3 and 6 and shading in between.
number line with open dot at negative 3 with shading to the left and an open dot at 6 with shading to the right.
number line with open dots at negative 2 and 5 with shading in between.
number line with shading everywhere.
4p + 1 > -11 or 6p + 3 < 39
-1 -1 -3 -3
4p > -12 6p < 36
[tex]\frac{4p}{4} > \frac{-12}{4}[/tex] [tex]\frac{6p}{6} < \frac{36}{6}[/tex]
y > -3 y < 6
Graph: -3 o-------------------------o 6
None of the choices you provided are correct. If you meant to type in ≥ and ≤ instead of > and <, then the first answer is correct.
Answer: D
Step-by-step explanation:
A recipe for chocolate chip cookie calls for 3 4 th of a cup of brown sugar to make 10 cookies how much brown sugar would be needed to make 48 cookies
Answer: 3.6 cups or 3 3/5 cups
Step-by-step explanation: what i would do here is set up a proportion. Change 3/4c to .75 cups as it’s easier to place in a proportion (and less confusing).. cross multiply .... (.75 x 48= 36) then divide 36 by 10 and that will give you x
Slope=2/3 contains (6,-1)
The answer you are looking for is Y = 2/3X - 5.
To find this, you must fill in the equation Y = MX + B, where Y = -1, M = 2/3, and X = 6. Filling in for those variables, you should get -1 = 2/3(6) + B. Now, you solve for B. Multiply 6 and 2/3 together, by putting 6 over 1 and multiplying straight across. 6 times 2 is 12 and 1 times 3 equals. This will give you 12/3, which simplified, is 4. Then, subtract 4 from both sides to get B = -5. Finally, fill in Y = MX + B, but this time only fill in M (2/3) and B (-5). This making Y = 2/3X - 5 the answer. Here's a graph to show this is the correct answer.
I hope this helps!
what is the function rule for the line?
For these types of problems, there is a shortcut to eliminating an answer choice, look at the Y intercepts in the different choices and compare that to the graph. In this case, you can eliminate A, because the line crosses at y=-2.
Now start at -2 on the y intercept and see which answer choice will make you hit another point on the line.
B can be eliminated because because you rise 3 and run 2, since you run a positive number, that means you move to the right, so that will eliminate that answer, but lead you to the correct one. You can tell that rising positive 3 was correct, but now you have to move to the left so that would be a negative and you have to move 2 spaces.
So combining those two thoughts, -3/2 is what you would be looking for making D your answer.
Hope this helps, comment any questions you may have.
Quadrilateral RSTU has vertices R(1,3), S(4,1), T(1,-3) and U(-2,-1). Is it true or false that this is a rectangle because the diagonals are congruent and the sides RS and ST are perpendicular?
Given vertices ofQuadrilateral RSTU as R(1,3), S(4,1), T(1,-3) and U(-2,-1).
We need to check if diagonals are congruent.
The coordinates of verticales diagonal RT are R(1,3) and T(1,-3).
The coordinates of verticales diagonal SU are S(4,1), and U(-2,-1),
By applying distance formula:
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
RT = [tex]=\sqrt{\left(1-1\right)^2+\left(-3-3\right)^2}[/tex]=[tex]\sqrt{36}[/tex]
RT = 6
SU [tex]=\sqrt{\left(-2-4\right)^2+\left(-1-1\right)^2}[/tex].
[tex]=2\sqrt{10}[/tex].
Diagonal RT is not congruent to Diagonal SU.
Therefore, Quadrilateral RSTU is not a rectangle because the diagonals are not congruent.
So, it is False.
Final answer:
The quadrilateral RSTU is not a rectangle due to not having all right angles, making it a parallelogram.
Explanation:
The given quadrilateral RSTU is not a rectangle. To determine if it's a rectangle, we need to check if all angles are right angles, which is not the case here even if the diagonals are congruent and RS and ST are perpendicular.
Since the angles are not all right angles, the shape formed is a parallelogram. A rectangle must have all angles as right angles, so these conditions do not define a rectangle.
To lose one pound of fat, a 200-pound person must burn 3,500 calories. If that person burns 180 calories by walking for 30 minutes, how many hours and minutes does the person have to walk to lose two pounds? Round your answer to the nearest minute.
Answer: 19.44 hours or 19 hours and 26 minutes.
Step-by-step explanation:
1. To lose 1 pound, a 200-person must burn 3,500 calories. Therefore, to lose 2 pounds that person must burn 7,000 calories.
2. If the person burns 180 calories by walking for 30 minutes or [tex]\frac{1}{2}[/tex] hour, to calculate the time in hours the person has to walk to lose 2 pounds, you can multiply 7,000 calories by [tex]\frac{1}{2}[/tex] hour and divide by 180 calories:
[tex]time=\frac{(7,000Cal)(\frac{1}{2}h)}{180Cal}\\time=19.44h[/tex]
3. You have:
[tex]minutes=(0.44)(60)\\minutes=26.4min\\minutes=26min[/tex]
4. Then, you can express it as following:
19 hours and 26 minutes
To lose two pounds, a 200-pound person who burns 180 calories per 30-minute walk needs to burn 7,000 calories in total. This can be found by dividing the total amount to burn (7,000) by the amount burned per walk (180) and converting the result from minutes to hours and minutes.
Explanation:To determine how much time this 200-pound person needs to walk to lose two pounds of weight, we need to first calculate the total amount of calories he or she needs to burn. Since it requires a 3,500-calorie deficit to lose one pound of weight, two pounds would require burning a total of 7,000 calories. Given that this person burns 180 calories per 30-minute walk, we can calculate the total amount of time required to burn these calories by walking. First, calculate the total walks needed by dividing the total calories to burn (7,000) by the amount of calories burned per walk (180). Then convert the result from minutes to hours and minutes.
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50 Pts
jordan and sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up or the trip and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla only has enough to make 40 necklaces.
A) write two constraints to model the problem. let x represent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells.
B) can Sharla afford the down payment with the money she earns selling all of her necklaces? explain your answer.
Thank you
A) 25x+15y=650
25x+15(40)=650
Or it could be 25x=650 and 15y=650
B) No because she makes $15 for every necklace which she only has 40 necklaces 15x40=600
A) 25x+15y=650 i think its correct
Megan baby-sat this weekend. She earned $12 an hour plus an additional $32. If she made a total of $140, how long did she work for?
Megan worked for a total of 9 hours.
Explanation:To find how long Megan worked, we need to subtract the additional amount she earned from the total amount she made. Let's say she worked for x hours. Her earnings can be calculated using the equation:
12x + 32 = 140. Subtracting 32 from both sides, we get 12x = 108. Dividing both sides by 12, we find that x = 9.
Therefore, Megan worked for 9 hours.
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Riley has a piece of yarn that is 6 1 2 ft long. She wants to cut the yarn into sections that are each 1 4 ft long. How many sections will the yarn be cut into?
Answer: The yarn will be cut into 26 sections.
Step-by-step explanation:
Since we have given that
Length of piece of yarn = [tex]6\dfrac{1}{2}=\dfrac{13}{2}\ feet[/tex]
Length of section = [tex]\dfrac{1}{4}\ feet[/tex]
We need to find the number of sections that will be cut into:
So, the number of sections would be
[tex]\dfrac{13}{2}\div \dfrac{1}{4}\\\\=\dfrac{13}{2}\times \dfrac{4}{1}\\\\=13\times 2\\\\=26[/tex]
Hence, the yarn will be cut into 26 sections.
Can You help me with this question please.
Thanks In Advance.
y = [tex]\frac{3}{2}[/tex] x + 3
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 4, - 3)
m = [tex]\frac{-3-3}{-4-0}[/tex] = [tex]\frac{-6}{-4}[/tex] = [tex]\frac{3}{2}[/tex]
since the y-intercept is (0,3 ) then c = 3
y = [tex]\frac{3}{2}[/tex] x + 3 is the equation of the line
A rabbit is 4m away from its burrow. Each hop takes it 0.4m farther from the burrow. The following diagram shows that there is a tasty plant that is 6m from the burrow. Which equation can we use to determine h, the number of hops it takes the rabbit to reach the plant?
A 6h+0.4=4
B 4h+0.4=6
C 4+0.4h=6
D 6+0.4h=4
Answer:
The correct option is: C. [tex]4+0.4h = 6[/tex]
Step-by-step explanation:
Each hop takes it 0.4 meter further from the burrow.
If the number of hops the rabbits takes to reach the plant is [tex]h[/tex], then the total distance it traveled to reach the plant will be: [tex]0.4h[/tex] meters.
As the rabbit was initially 4 meter away from it's burrow, so the distance from the burrow to the plant will be: [tex](4+0.4h) meters[/tex]
Given that, the plant is 6 meters away from the burrow.
So, the equation that we can use to determine the number of hops it takes the rabbit to reach the plant will be: [tex]4+0.4h = 6[/tex]
Answer:
C
Step-by-step explanation:
Because it is boyyyys
linda has 24 students in her class and she wants each student to have 3 ice cream sandwiches if there are 12 sandwiches in each box how many boxes should she buy
24 x 3 = 72
72/12 = 6
She should buy 6 boxes.
Hope this Helps!!
6 boxes
24x3=72
72/12=6
Please help me!! You don’t need a number just an expression to find the variable
Solve for y. Note the equal sign. What you do to one side, you do to the other. Isolate the y. Do the opposite of PEMDAS.
First, subtract x from both sides
y²z + x (-x) = b (-x)
y²z = b - x
Next, divide z from both sides
(y²z)/z = (b - x)/z
y² = (b - x)/z
Finally, to fully isolate the x, root both sides
√(y²) = √((b - x)/z)
y = √((b - x)/z)
y = √((b - x)/z) is your answer
hope this helps
The answer, I’ve been stuck on this and stressed out.
10 times that should be the answer
PLEASE HELP!! QUESTION IS ON THE PHOTO!!
Answer:
Option 4: [tex]\frac{8\frac{1}{2} }{\frac{5}{6} } =x[/tex]
Step-by-step explanation:
Total length of the board = [tex]8\frac{1}{2}[/tex] feet
Length of the smaller board to be cut = [tex]\frac{5}{6}[/tex] feet
So,
[tex]8\frac{1}{2} =\frac{5}{6} +\frac{5}{6} +\frac{5}{6} ....x[/tex] times.
[tex]8\frac{1}{2} =x(\frac{5}{6} )[/tex]
[tex]\frac{8\frac{1}{2} }{\frac{5}{6} } =x[/tex]
The length of the flat screen tv is 5 inches less than 3 times it's width. If the perimeter of the tv is 150 inches, find the dimensions
AS we don't know the width so let consider width=x inches
According to given condition
length = (3x -5) inches
TV screen is rectangular shaped so
Perimeter= 2( length +width) =2{(3x-5)+ (x)} equation 1
also given Perimeter = 150 inches equation 2
comparing equation 1 &2
2{(3x-5)+ (x)} =150
2{3x-5+x} =150
2{4x-5} =150
8x-10 =150
Adding 10 both sides
8x -10 +10 =150+10
8x=160
dividing 8 both sides
8x/8= 160/ 8
x= 20 inches width of screen.
length =( 3x-5) ={3(20) -5}
=60-5
length =55
If the The length of the flat screen tv is 5 inches less than 3 times it's width, and the perimeter is 150 inches, then the dimension of the TV screen = 55 inches by 20 inches
Let the length of flat screen tv be represented by L
Let the width of the flat screen tv be represented by W
Three times the width of the flat TV screen = 3W
The length of the flat screen tv is 5 inches less than 3 times it's width.
L = 3W - 5........................(1)
The TV screen is rectangular in shape
The perimeter of the TV screen is given by the formula:
P = 2(L + W)
The perimeter of the TV is 150 inches
P = 150 inches
150 = 2(L + W)
L + W = 150/2
L + W = 75..........(2)
Substitute equation (1) into equation (2)
3W - 5 + W = 75
Collect like terms
3W + W = 75 + 5
4W = 80
W = 80/4
W = 20
Substitute W = 20 into equation (1)
L = 3W - 5
L = 3(20) - 5
L = 60 - 5
L = 55
The width of the TV screen = 20 inches
The length of the TV screen = 55 inches
The dimension of the TV screen = 55 inches by 20 inches
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Indicate whether the lines are parallel, perpendicular, or neither. Justify your
answer.
a. y = 4x − 1 and 12x = 3y + 7
These lines would be perpendicular.
If we divide 3y+7 by 12, we would get 1/4y+7/12
Now, if we re arange for y, we get: y=-1/4x+7/3
In this case, the y intercept (7/3) does not matter, only the slope does. The slope must be the opposite reciprical of the other slope. For instace if the slope was 4, the perpendicular lines slope must be -1/4. That is the exact case we have above.
Really hope that I helped :)
Let me know if you have any furthere questions!
-CSX
Another way to write this problem: mq-rp=d
d + mq = rp
or
rp + d = mq
I need help please!
simplify:
Select one:
a. none of these
b. x20
c. x120
d. x14
It would be (x^7)*(x^7)
Well, first, you must simplify each monomial and get rid of the parentheses. This can be done by adding the exponents together, as [tex]x^3[/tex] is being multiplied by [tex]4[/tex]. The same goes for [tex]x^2[/tex]. This would give you the expression: [tex]x^7*x^7[/tex]
Once again, add the two exponents together and you get your answer: [tex]x^1^4[/tex]
Ugh this is bothering me
Simplify completely
(h12h4)3
Answer:
it is not h^48. I just took the test and its h^24!
Step-by-step explanation:
How does finding the square root of a number compare to finding the cube root of a number? Use the number 64 in your explanation
Answer:
The square-root of a number has 2 same factors being multiplied to get that number while a cubic-root of a number has 3 same factors being multiplied to get that number. For example, the square-root of 64 is 8 because 8 x 8 is 64. However, the cubic-root of 64 is 4 since 4 x 4 = 16 x 4 = 64.
Step-by-step explanation:
Finding the square-root of a number means finding two same numbers that when multiplied equal one number, while finding the cubic-root of a number means finding three same numbers that when multiplied equal one number. For example, the square-root of 64 is 8 because 8 x 8 is 64. However, the cubic-root of 64 is 4 since 4 x 4 = 16 x 4 = 64.
The square root of a number is found by multiplying it by itself, while the cube root is found by multiplying it by itself three times.
Explanation:Finding the square root of a number is the process of finding a number that when multiplied by itself gives the original number. For example, the square root of 64 is 8, because 8 x 8 = 64.
Finding the cube root of a number is the process of finding a number that when multiplied by itself three times gives the original number. For example, the cube root of 64 is 4, because 4 x 4 x 4 = 64.
So, the main difference is that the square root involves multiplying a number by itself once, while the cube root involves multiplying a number by itself three times.
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Given the table of candy distibutions below, find P(not green), the probability of selecting anything but a green candy at random from a large bag
Answer: 0.84
Step-by-step explanation:
From the given table of probability distribution P (green)= 0.16
Since , the sum of all the probabilities of all the events in a particular probability distribution is 1.
Therefore, The probability of selecting anything but a green candy at random from a large bag is given by :-
[tex]\text{P(not green)=1-P(green)}\\\\\Rightarrow\text{P(not green)}=1-0.16\\\\\Rightarrow\text{P(not green)}=0.84[/tex]
Hence, the probability of selecting anything but a green candy at random from a large bag = 0.84
beef cost $6.00 per pound and the chicken cost 4.50 per pound. he bought a total of 18 lbs and spent $96. how much of each type of meat did he purchase?
Wrong answer :) Please check others