Answer:
11.34 m³
Explanation:
The volume of a right rectangular prism can be calculated as:
[tex]\text{Volume}=\text{Height}\times\text{ Length}\times\text{ Width}[/tex]So, replacing the height by 3.6 m, the length by 2.1 m, and the width by 1.5m, we get:
[tex]\begin{gathered} \text{Volume}=3.6\text{ m }\times2.1\text{ m }\times1.5\text{ m } \\ \text{Volume = 11.34 m}^3 \end{gathered}[/tex]Therefore, the volume of the prism is 11.34 m³
An automobile travels 415 miles on 16 2/3 gallons of gasoline.
a) How many miles per gallon does the car get on the trip? (Enter your answer as a simplified mixed number.)
b) How many gallons would be required for the car to travel 498 miles?
Choose the correct ordering of the numbers below from greatest to least.L. 779.56M. 29.7023N. 7.8695O. 0.8436P. 70.7540
When you order a number, you must check the number most in the left. The number L and the number M for example,
L. 779.56
M. 029.7023
In the hundreds place, L has a '7', and M has a '0', this means L is bigger than M.
Doing the same procedure with the other, we get the following order:
[tex]\begin{gathered} 779.56>70.7540>29.7023>7.8695>0.8436 \\ L>P>M>N>O \end{gathered}[/tex]Put the correct number in each box 1/7 = 4/? = ?/56
Answer: 1/7 = 4/28 = 8/56
Step-by-step explanation: 7 timestables
Answer:
1/7=4/28=8/56
Step-by-step explanation:
From the pattern of the question we can see that the numerator of the second fraction is 4 and the previous fraction's numerator is 1 that means the fraction has been multiplied by 4. Therefore multiplying the numerator and denominator results in the answer 4/28. For the last fraction we can see that the denominator is 56 and is the double of 28 therefore doubling the whole second fraction we get our answer as 8/56. Overall equating all the three fractions we get the same answer 1/7 after minimizing the fraction.
Username: TNakashrai
10 Caleb divides powers of 10 using exponents . He says that 0.6 divided by increases the value of the 6. Do you agree with Caleb ? 10 ^ 2 Explain your thinking
I disagree with Caleb because the value decreased after the quotients are carried out
How to determine the true statement?From the question, the statement is given as
He says that 0.6 divided by 10² increases the value of the 6.
The mathematical expression of the above statement is represented as
0.6 divided by 10²
So, we have
0.6/10²
When the above quotient is evaluated, we have
0.6/10² = 0.006
The above result is different from Caleb's reasoning
This is so because 0.6 divided by 10² decreases the value of the 0.006, instead of increasing the value to 6, as stated by Caleb
Hence, Caleb's reasoning is incorrect
Read more about scientific numbers at
https://brainly.com/question/27862246
#SPJ1
Complete question
Caleb divides powers of 10 using exponents. He says that 0.6 divided by 10² increases the value of the 6.
Do you agree with Caleb? Explain your thinking
Factor 3z^2(8z^2-14z+3)
Answer:
3z²(4z-1)(2z-3)
Step-by-step explanation:
Factor 8z²-14z+3
8z²-14z+3 = (4z-1)(2z-3)
So 3z² (8z²-14z+3)
= 3z²(4z-1)(2z-3)
I only need help with the gauss elimination and back substitution, and cramers rule. I know hwo to do everything else.
To solve the equation by Gauss elimination method first convert the equation in matrix form.
The cramers rule is as follows;
y + 3 = 2/5(x + 5) , put that into standard form
Given:
[tex]y+3=\frac{2}{5}(x+5)[/tex]The standard form of the linear equation is,
[tex]Ax+By=C[/tex]Simplify the given equation,
[tex]\begin{gathered} y+3=\frac{2}{5}(x+5) \\ 5(y+3)=2(x+5) \\ 5y+15=2x+10 \\ 2x-5y=15-10 \\ 2x-5y=5 \end{gathered}[/tex]Answer: Standard form is 2x - 5y = 5
What is the range shown in the graph below ?
Take into account that the range are all availables values of the function, that is, available values of the y coordinate in the graph.
As you can notice, such values are in the following interval:
range: (-∞,8]
Write a quadratic function in standard form, with a leading coefficient of 1, given x-intercepts 7 and 10. Use "y" as the dependent variable
and "x" as the independent variable.
Standard form of quadratic function with leading coefficient 1,
x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
As given in the question,
Given :
y is the dependent variable of the required quadratic function.
x is the independent variable of the required quadratic function.
Leading coefficient of quadratic function is 1
X-intercept of the required function is 7 and 10
Standard form of required quadratic function is equal to
y = k (x-a)(x -b)
Here k=1 , a=7 , b=10
y = 1 (x -7)(x - 10)
⇒ y = x² -7x -10x +70
⇒ y= x² -17x +70
Therefore, standard form of quadratic function with leading coefficient 1, x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
Learn more about quadratic function here
brainly.com/question/27958964
#SPJ1
Can anyone answer this question fast?
how do i do square root of 24 on the simplified radical form
Re-write the question as :
[tex]\sqrt{24}[/tex]This can further be written using factors of 24 as;
[tex]\sqrt{6\ast4}[/tex]Separate as :
Evaluate. 0⁴= please
I GIVE BRAINIEST
Does the equation y-250x=500 represent the same relationship between the distance from the start of the trail and the elevation? Explain your reasoning pls
The equation of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Isolate y from the given equation to write it in slope-intercept form:
[tex]\begin{gathered} y-250x=500 \\ \Rightarrow y=250x+500 \end{gathered}[/tex]The given equation corresponds to a line with slope 250 and y-intercept 500.
From the image, we can see that the y-intercept is indeed 500, since it is the value of y when x=0.
Notice also that for each increase of 1 unit of the variable x, the variable y increases 250 units. Then, the slope of the graph is 250, the same as the slope of the equation.
We can also check if the equation represents the same line as the graph by evaluating th
MapsQuestion 120 ptsIf a recipe calls for 58 ounces of pecans andthere are 16 ounces in 2 cups, how many pecanswill you need?
the recipe needed = 58 ounces of pecans
we have 16 ounces in 2 cups,
so we need
58 - 16 = 42 ounces
so we need 42 ounces of pecans.
GARDENING Molly's school is planning a school-based community garden with the diagram shownIf the school has 64 yards of fencing for the rectangular garden, use a system of equations and a graphing calculator to find the value of Then find the dimensions of the garden.
The value of x is 5 yards and the length and width of the garden is 20 yards and 12 yards respectively.
Given, the school has 64 yards of fencing for the rectangular garden.
we know that, the perimeter of the rectangle is the sum of twice the length and twice the width.
length (l) = x²-5
width (w) = 4x-8
therefore, 2(l+w) = 64
⇒ 2(x²-5+4x-8) = 64
⇒ 2(x²+4x-13) = 64
⇒ 2x²+8x-26 = 64
⇒2x²+8x-26-64 = 0
⇒2x²+8x-90 = 0
divide the equation by 2.
⇒ x²+4x-45=0
⇒ x²+9x-5x-45 = 0
⇒ x(x+9) - 5(x+9) = 0
⇒ (x+9) (x-5)
⇒ x = -9 or x = 5
therefore, x cannot be negative,
hence x = 5 yards.
therefore, l = x²-5
l = 5² - 5
l = 25-5
l = 20 yards.
w = 4x-8
w = 4(5) - 8
w = 20-8
w = 12 yards.
Hence we get the value of x as 5 yards and the dimensions of the garden as 20 yards by 12 yards,
Learn more about system of equations here:
brainly.com/question/13729904
#SPJ1
Hello! Vectors u and v are shown in the graph. What is -3(u x v)?
Explanation
The values of the vectors are shown below
Thus
[tex]\begin{gathered} u=(6,5) \\ v=(-6,-10) \end{gathered}[/tex]Thus to get -3(u.v) will be
[tex]\begin{gathered} step\text{ 1} \\ find\text{ the dot product} \\ u.v=6(-6)+5(-10) \\ u.v=-36-50 \\ u.v=-86 \end{gathered}[/tex]The next step will be
[tex]\begin{gathered} -3(u.v)=-3\times-86=258 \\ \\ -3(u.v)=258 \end{gathered}[/tex]The answer will be
the rest of the question say find the length of the whole secant of the bottom
According to the Intersecting Secants Theorem,
[tex]\begin{gathered} x\times6=(12+8)\times8 \\ 6x=20\times8 \\ x=\frac{80}{3} \\ x=26.\bar{66} \\ x\approx26.67 \end{gathered}[/tex]Thus, the first option is the correct choice.
5/6x-2/3(x-2) + 1/2 please helppp
Answer:38
Step-by-step explanation:
XZ¯¯¯¯¯¯¯¯ has a point Y between points X and Z. XY=17, YZ=4x+9, and XZ=11x−9.
Applying the segment addition postulate, the value of x = 5.
What is the Segment Addition Postulate?According to the segment addition postulate, if three lines, X, Y, and Z are collinear points, that is they lie on a straight line such that Y is between points X and Z, then the sum of the lengths of segments XY and YZ would be equal to the length of segment XZ.
Therefore:
XY + YZ = XZ [segment addition postulate]
Given:
XY = 17
YZ = 4x + 9
XZ = 11x − 9.
Substitute
17 + 4x + 9 = 11x - 9
26 + 4x = 11x - 9
26 + 9 = 11x - 4x
35 = 7x
35/7 = x
x = 5
Learn more about segment addition postulate on:
https://brainly.com/question/2134445
#SPJ1
The Whistling Straits Corporation needs to raise $40 million to finance its expansion intonew markets. The company will sell new shares of equity via a general cash offering toraise the needed funds. If the offer price is $35 per share and the company'sunderwriters charge a 11 percent spread, how many shares need to be sold?
Solution
Explanation:
Total Finance Needed = $40,000,000
Offer price per share = $35 per share
Charges of underwriter = 11%
Total Number of shares needed to be sold = ( $40,000,000 / $35 ) x 111%
Total Number of shares needed to be sold = 1,142,857 x 111%
Total Number of shares needed to be sold = 1,267,571 shares
The Whistling Straits Corporation needs 1,267,571 shares to raise $40 million
Use the diagram to answer the question. 15 ft 120 ft2 10 ft A rectangular yard contains a 120-square-foot garden. If seeds are scattered uniformly over the yard, what is the probability that a seed lands in the garden?
area of the rectangle
[tex]\begin{gathered} \text{area}=\text{length}\times width \\ \text{area}=15\times10=150 \end{gathered}[/tex]area of rectangle is 150 sq ft, therefore the probability that a seed lands in the garden is
[tex]\frac{area\text{ garden}}{area\text{ rectangle}}=\frac{120}{150}=\frac{4}{5}[/tex]answer: 4/5
A college student realized that he was spending too much money on music. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towardsmusic. How much can he spend in December, taking into consideration that in the other 4 months he spent $20, $70, S30, and $85, respectively? Round your answerto two decimal places. If necessary
The mean is given by the sum of all the months divided by the number of months.
Then:
Let's set x for the spending money for December.
There are 5 months.
Hence:
[tex]\operatorname{mean}=\frac{20+70+30+85+x}{5}[/tex]We need to have a mean equal to $50. Set mean = 50.
[tex]50=\frac{20+70+30+85+x}{5}[/tex]Solve for x:
[tex]\begin{gathered} 50=\frac{20+70+30+85+x}{5} \\ 50=\frac{205+x}{5} \\ 5\cdot50=205+x \\ 250=205+x \\ \text{Therefore:} \\ x=250-205 \\ x=45 \end{gathered}[/tex]Hence, If the student wants to complete his goal, he will need to spend $45 in December.
Evaluate the expression when m = -4. M^2+6m+9
The answer is 1
please help me solve. I have 81 for blank 1 and 9 for blank 2. it is incorrect
We can further simplify
[tex]\sqrt[]{27}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3\text{ x 9}} \\ \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x }\sqrt[]{9} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x 3 = 3 x }\sqrt[]{3} \\ \sqrt[]{27}\text{ = 3 }\sqrt[]{3} \end{gathered}[/tex][tex]\sqrt[]{3}\text{ x }\sqrt[]{27\text{ }}\text{ = }\sqrt[]{3}\text{ x 3}\sqrt[]{3}[/tex]The answers for the blank spaces are
[tex]\sqrt[]{3}\text{ and 3}\sqrt[]{3}[/tex]A right isosceles triangle has an area of 40.5 cm2. How tall is it?
Area = 40 cm^2
base = ?
height = x
Area = base * height / 2
bh = 2(40.5)
bh = 81 cm^2
81 3
27 3
9 3
3 3 height = 3 x3 x 3 base = 3
1
The height must be 27 cm and the base 3 cm.
What is the answer with a posible fraction remainder3.8/21.85
The solution with a potential fraction remainder for the given fraction, 3.8/21.85, is 0.
How to find the remainder?By shifting the decimal point 1 places to the right, you can convert the divisor 3.8 to a whole number. Then, move the decimal point in the dividend by one place to the right, keeping the same position.
what do you understand by remainder ?The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.
These equations follow:
218.5 ÷ 38 = 5.750
because of this:
21.85 ÷ 3.8 = 5.750
To three decimal places, both calculations.
0 0 5. 7 5 0
3 8 √2 1 8. 5 0 0
− 0
2 1
− 0
2 1 8
− 1 9 0
2 8 5
− 2 6 6
1 9 0
− 1 9 0
0 0
− 0
0
The answer is 0.
To learn more about remainders here-
brainly.com/question/1141386
#SPJ13
An equality that represents numbers that are not a solution of x-1.2>2.8
The solution is x> 4 or x ∈(4,∞)
Here equality given is
x - 1.2> 2.8
Rearrange the variable to the left side of the equation
x > 2.8 + 1.2
Calculate the sum
x > 4
Or we can also say
x ∈ (4,∞)
Therefore the range of x is x∈ (4,∞).
To know more about the range of the solution refer to the link given below:
https://brainly.com/question/2264373
#SPJ1
Find the intersection points of f(x) = (x + 7)(x - 5) and g(x) = x-5.
510
Answer:
-7
Step-by-step explanation:
all answers are in the picture
Complete Complete the following tick -tac-toe board to find the three in a row there is only one correct way to make the tick-tac-toe, three in row! The code to unlock the puzzle will be the product of the three the following three puzzle Tic tac toe
At the end of a party, 3/4 cup of smoked fish dip is left. Jim divides 4/5 of the leftover smoked fish dip equally between 2 friends. How much dip does each friend get?
Each friend gets 3/10 or 0.3 dips if, at the end of a party, 3/4 cup of smoked fish dip is left.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let each freind get x part.
The 3/4 part dipped:
The value of x can be found as follows:
x = (3/4)(4/5) ÷ 2
x = 3/(5×2)
x = 3/10
x = 0.3
Thus, each friend gets 3/10 or 0.3 dips if, at the end of a party, 3/4 cup of smoked fish dip is left.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ1