Answer:
$1050
Step-by-step explanation:
To solve, multiply your two expenses against your $6000 and find the difference.
The man spends 1/5 of his salary on children's education.
To find how much he spends on his children's education in dollars, multiply 1/5 against $6000.
[tex]\frac{1}{5} *6000\\1200[/tex]
The man spends $1200 on children's education.
The man spends 5/8 of his salary on his aged mother and unemployed sister.
Repeat the same process as the first step, this time multiplying 5/8 against $6000.
[tex]\frac{5}{8} *6000\\3750[/tex]
The man spends $3750 on his aged mother and unemployed sister.
Add these two expenses together.
[tex]1200+3750\\4950[/tex]
The man has combined expenses of $4950.
To find how much money he has left, subtract his expenses from his $6000 income.
[tex]6000-4950\\1050[/tex]
The man has $1050 remaining.
The smiths have saved $25,000 toward the purchase of a new car. If the sales tax is 5%, the purchase price of smiths new car before taxes cannot exceed what
Answer:
26,250
Step-by-step explanation:
25,000 + 5% = 26,250
:) please mark Brainliest
The Smiths' new car purchase price before taxes cannot exceed $23,809.52 considering they have $25,000 and need to pay a 5% sales tax on the purchase.
To calculate the maximum purchase price of the new car before taxes that the Smiths can afford, we need to account for the 5% sales tax they will have to pay on top of the purchase price. Since the Smiths have saved $25,000, this is the total amount they have available to pay for the car including the sales tax.
To find the purchase price before tax, call this price 'P'. The total cost including the sales tax will be P + 0.05P (which is the sales tax). This total cost must not exceed $25,000. Therefore, we can set up the following equation:
1.05P <= $25,000
Divide both sides of the equation by 1.05 to isolate P:
P <= $25,000 / 1.05
P <= $23,809.52
So, the purchase price of the Smiths' new car before taxes cannot exceed $23,809.52.
What is the volume of a shipping cube with dimensions of 3 1/2 feet
Answer:
the answer is 42.875
Step-by-step explanation:
3.5^3 = 42.875
Answer:
[tex]\large\boxed{V=42\dfrac{7}{8}\ ft^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cube:
[tex]V=a^3[/tex]
a - edge
We have
[tex]a=3\dfrac{1}{2}\ ft[/tex]
Convert to the improper fraction:
[tex]a=\dfrac{3\cdot2+1}{2}=\dfrac{7}{2}\ ft[/tex]
Substitute to the formula of a volume:
[tex]V=\left(\dfrac{7}{2}\right)^3=\dfrac{7^3}{2^3}=\dfrac{343}{8}=42\dfrac{7}{8}\ ft^3[/tex]
A triangle has two angles measuring 90 and 50%, calculate the third angle of the triangle,
a 50
C. 45
b. 40%
d. 750
Answer:
40°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for third angle
third angle = 180° - (90 + 50)° = 180° - 140° = 40°
Answer: B. 40
Step-by-step explanation: A triangle’s angles will always add up to 180 degrees. Add the 2 angles that are given. 90 + 50 = 140. Subtract this number from 180. 180 - 140 = 40. The third angle is 40 degrees.
(polynomials) multiply. (x^2-5x)(2x^2+x-3)
A. 2x^4 - 9x^3 - 9x^2 - 15x
B. 2x^4 + 9x^3 - 8x^2 + 15x
C. 4x^4 + 9x^3 - 8x^2 + 15x
D. 2x^4 - 9x^3 - 8x^2 + 15x
Answer:
2x^4 - 9x^3 -8x^2 + 15x
Step-by-step explanation:
(x^2-5x)(2x^2+x-3) distribute first
2x^4
x^2 + x = x^3
5 * 2x^2 x= 10x^3
5x^1+1 = 5x^2
5 * 3x = 15x Put them all together
2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x Like terms
2x^4 + x^3 -10x^3 - 3x^2- 5x^2 + 15x Add similar terms
= 2x^4 + x^3 - 10x^3 - 8x^2 + 15x more adding terms
2x^4 - 9x^3 -8x^2 + 15x
Hope my answer has helped you, if not i'm sorry.
For this case we must multiply the following expression:
[tex](x ^ 2-5x) (2x ^ 2 + x-3)[/tex]
We apply distributive property term to term taking into account that:
[tex]+ * - = -\\- * - = +\\x ^ 2 * 2x ^ 2 + x ^ 2 * x-x ^ 2 * 3-5x * 2x ^ 2-5x * x + 5x * 3 =[/tex]
For powers of the same base, we place the same base and add the exponents:
[tex]2x ^ 4 + x ^ 3-3x ^ 2-10x ^ 3-5x ^ 2 + 15x =[/tex]
We add similar terms:
[tex]2x ^ 4-9x ^ 3-8x ^ 2 + 15x[/tex]
Answer:
OPTION D
[tex]2x ^ 4-9x ^ 3-8x ^ 2 + 15x[/tex]
Two angles are complementary, and Angle A is 6° more than Angle B. What is the measure of Angle A?
6°
42°
45°
48°
Complementary angle add up to 90 degrees.
Angle A = x + 6
Angle B = x
They both add up to 90.
x + 6 + x = 90
2x + 6 = 90
2x = 90 - 6
2x = 84
x = 84/2
x = 42
Angle A = x + 6
Angle A = 42 + 6
Angle A = 48 degrees
For Sophia’s graduation party, several tables of the same width will be arranged end to end to form a serving table with a total area of 75 ft 2 . The total length of the tables will be two more than three times the width. Find the length and width of the serving table so that Sophia can purchase the correct table cloth. Round your answers to the nearest tenth
Answer:
The length is 16.1 ft and the width is 4.7 ft
Step-by-step explanation:
Let
x -----> the total length of the tables
y -----> the width of the tables
we know that
The area is equal to
[tex]A=xy[/tex]
[tex]A=75\ ft^{2}[/tex]
so
[tex]75=xy[/tex] -----> equation A
[tex]x=3y+2[/tex] -----> equation B
substitute equation B in equation A
[tex]75=(3y+2)y[/tex]
[tex]3y^{2} +2y-75=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=4.7\ ft[/tex]
Find the value of x
[tex]x=3(4.7)+2=16.1\ ft[/tex]
therefore
The length is 16.1 ft and the width is 4.7 ft
Answer:
The length and width of the serving table is 16.1 ft and 4.7 ft respectively.
Step-by-step explanation:
Consider the provided information.
Let the width of the table is x and length of the table is y.
The total length of the tables will be two more than three times the width.
This can be written as:
y = 2+3x
The area of the table is 75 ²ft
The area of rectangle is:
length × width = Area
Substitute width = x and length = 2+3x in above formula.
(x)(2+3x) = 75
2x+3x²-75 = 0
3x²+2x-75 = 0
The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute a=3, b=2 and c=-75 in above formula.
[tex]x_{1,2}=\frac{-2\pm\sqrt{2^2-4(3)(-75)}}{2(3)}[/tex]
[tex]x_{1,2}=\frac{-2\pm\sqrt{904}}{6}[/tex]
[tex]x_{1,2}=\frac{-2\pm30.07}{6}[/tex]
[tex]x_{1}=\frac{-2+30.07}{6}[/tex]
Ignore the negative value of x as width should be a positive number.
[tex]x=4.7\ ft[/tex]
Now substitute the value of x in y = 2+3x.
y = 2+3(4.7)
y = 16.1 ft
Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.
What type of triangle has side lengths 4, [tex]\sqrt{415} \\[/tex], and 16?
Step-by-step explanation:
It is impossible for a triangle to have side lengths of 4, √415, and 16.
The sum of the shortest two sides must be greater than the longest side. However, 4 + 16 < √415.
It is impossible to make a triangle with side lengths 4, √415, and 16 because the two side length of the triangle is always greater than the third length of the triangle.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have side lengths of a triangle.
As we know from the definition of the triangle the sum of the two side length of the triangle is always greater than the third length of the triangle.
Also, the sum of the interior angle of a triangle is 180 degrees.
As the three lengths are 4, √415, and 16
AB + BC < AC
Let suppose:
AB = 4 units
BC = 16 units
AC = √415 units
4 + 16 < √415
Thus, it is impossible to make a triangle with side lengths 4, √415, and 16.
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Solving a Quadratic Equation
Which statement is true about the equation (x – 4)(x + 2) = 16?
O The equation x – 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x2 – 2x – 8 = 0.
O The factored form of the equation is (x + 4)(x – 6) = 0.
o One solution of the equation is x = -6.
Answer:
The factored form of the equation is (x + 4)(x – 6) = 0.
Step-by-step explanation:
(x – 4)(x + 2) = 16
Foil the left side
x^2 +2x-4x-8 =16
Combine like terms
x^2 -2x-8 = 16
Subtract 16 from each side
x^2 -2x-8-16 =16-16
x^2 -2x-24 =0
Factor the left hand side
What two numbers multiply to -24 and add to -2
-6*4 =-24
-6+4 = -2
(x-6) (x+4) =0
Solving using the zero product property
x-6 =0 x+4=0
x=6 x=-4
Answer:
C: on ed
Step-by-step explanation:
If z is a standard normal variable, find the probability.
P(–0.73 < z < 2.27)
0.2211
0.4884
1.54
0.7557
Answer:
0.7557
Step-by-step explanation:
In this question use the Table of Standard Normal Probabilities for Negative z-scores and the Table of Standard Normal Probabilities for Positive z-scores
Where z=2.27 NORMDIST(2.27)=0.9884 (read from table for positive z-scores)
Where z=-0.73 NORMDIST(-0.73)=0.2327 (read from table for negative z-scores)
You know P(-0.73<z<2.27)= 0.9884-0.2327=0.7557
The probability that P(–0.73 < z < 2.27) is 0.7557.
The z score is used to determine by how many standard deviations, the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation,n= sample\ size\\\\\\[/tex]
From the normal distribution table, P(-0.73 ≤ z ≤ 2.27) = P(z < 2.27) - P(z<-0.73) = 0.9884 - 0.2327 = 0.7557
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Perform the indicated operation. Be sure the answer is reduced.
[tex] \frac{m}{n} . \frac{n}{p} \div \frac{p}{q} \\ = \frac{m}{p} \div \frac{p}{q} \\ = \frac{m}{p} . \frac{q}{p} \\ = \frac{mq}{ {p}^{2} } [/tex]
Hope it helps...
Regards;
Leukonov/Olegion.
Answer:
The correct answer is first option
mq/p²
Step-by-step explanation:
It is given that, (m/n) * (n/p) ÷ (p/q)
To find the simplified form of given expression
Let (m/n) * (n/p) ÷ (p/q) can be written as,
(m/n) * (n/p) ÷ (p/q) = (m/n) * (n/p) * (q/p)
= (m * n * q)/(n * p * q)
= (m * q)/(p * p)
= mq/p²
Therefore the correct answer is mq/p²
In △ABC, m∠A=15°, a=9, and b=12. Find c to the nearest tenth.
Answer:
=20.0
Step-by-step explanation:
We can first find the value of the angle at B using the sine formula.
a/sine A=b/Sin B
9/sin 15=12/sin B
Sin B=(12 sin 15)/9
Sin B=0.345
B=20.18°
Therefore angle C =180-(15+20.18)
=144.82°
a/Sin A=c/Sin C
9/Sin 15=c/Sin 144.82
c=(9 sin 144.82)/sin15
=20.0
A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which
equation gives the measure of the central angle, q?
To work out the central angle, you just re-arrange the equation for the length of an arc:
Equation for length of an arc:
[tex]\frac{angle}{360}[/tex] × [tex]diameter[/tex] × π = [tex]length of arc[/tex]
We can arrange this to work out the central angle, q. But first, lets substitute in all of the values that we know:
angle = q
diameter = 5 x 2 = 10 ft
length of arc = 7
[Substitute in]
[tex]\frac{q}{360}[/tex] × [tex]10[/tex]π = [tex]7[/tex] (Now just rearrange for q)
[tex]\frac{q}{360}[/tex] = [tex]\frac{7}{10\pi }[/tex] (multiply both sides by 360 to get q)
[tex]q[/tex] = [tex]\frac{7}{10\pi }[/tex] × [tex]360[/tex] (now just simplify)
[tex]q[/tex] = [tex]\frac{252}{\pi }[/tex]
= [tex]80.214[/tex] (rounded to 3 decimal places)
______________________________
Therefore:
The equation that gives you ange q is:
[tex]q[/tex] = [tex]\frac{length.of.arc}{diamater.times.\pi }[/tex] × [tex]360[/tex]
and q = 80.214 when all of the values are substituted in.
Answer:
B q=7/5
Step-by-step explanation:
Well Q=s/r and they said a Radius of 5 Which puts 5 at the bottom.
Then an arc length of 7 Which =S. so q=7/5
What is this in simplest rational exponent form
Answer:
[tex]4x[/tex]
Step-by-step explanation:
We want to find the simplest rational exponent form of
[tex]\sqrt{x} \cdot 4\sqrt{x}[/tex]
Recall that: [tex]\sqrt{a}=a^{\frac{1}{2} }[/tex]
We rewrite the expression in the exponent form to get:
[tex]x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}[/tex]
We can regroup the product to get:
[tex]4 x^{\frac{1}{2}\cdot x^{\frac{1}{2}[/tex]
We apply the rule: [tex]a^m\cdot a^n=a6{m+n}[/tex] to get:
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{\frac{1}{2}+\frac{1}{2}}[/tex]
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{1}[/tex]
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4x[/tex]
21
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The solution set of n2 - 14n = -45 is {
(Separate the solutions with a comma)
Answer:
the solution set of n2 - 14n = -45 is {5, 9}
Step-by-step explanation:
We have the following equation: n^2 - 14n = -45
Rearrange:
n^2 - 14n +45 = 0
Factorizing:
(n-9)(n-5) = 0
Therefore, the solution set of n2 - 14n = -45 is {5, 9}
What is the value of x in the equation-2/3x+9=4/3x-3
Answer:
6
Step-by-step explanation:
[tex]-\frac{2}{3} x+9=\frac{4}{3} x-3\\\\[/tex]
First, multiply both sides by 3.
[tex]-2x+27=4x-9\\[/tex]
Next, combine like terms.
[tex]-2x+27=4x-9\\-2x+36=4x\\36=6x[/tex]
Solve for x.
[tex]36=6x\\6=x[/tex]
The value of "x" in the equation is 6.
To find the value of "x" in the equation -2/3x + 9 = 4/3x - 3, we need to isolate "x" on one side of the equation. Let's solve step-by-step:
Step 1: Get rid of fractions by multiplying all terms by the least common multiple (LCM) of the denominators, which is 3.
3 * (-2/3x) + 3 * 9 = 3 * (4/3x) - 3 * 3
Simplify:
-2x + 27 = 4x - 9
Step 2: Move "4x" and "27" terms to one side and " -2x" and " -9" terms to the other side.
Add 2x to both sides:
-2x + 2x + 27 = 4x - 9 + 2x
Simplify:
27 = 6x - 9
Step 3: Move the constant term " -9" to the other side of the equation by adding 9 to both sides:
27 + 9 = 6x - 9 + 9
Simplify:
36 = 6x
Step 4: Solve for "x" by dividing both sides by 6:
x = 36 / 6
x = 6
The value of "x" in the equation is 6.
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El costo variable de fabricar una calculadora es de $2 y los costos fijos son de $105.
a. Determina la función lineal del costo total por fabricar x calculadora al día.
b. ¿Cuál es el costo por fabricar 50 calculadoras al día?
Answer:
a. [tex]c(x) = 2x + 105[/tex]
b. [tex]c(50) =\$205[/tex]
Step-by-step explanation:
The variable cost of $ 2 implies that for each manufactured calculator the total cost increases $ 2.
The fixed cost of $ 105 implies that regardless of the number of manufactured calculators there will always be a cost of $ 105.
If we call x the number of manufactured calculators then the total cost c(x) will be:
[tex]c(x) = 2x + 105[/tex]
Then, the cost of manufactured 50 calculators a day is:
[tex]c(50) = 2(50) + 105[/tex]
[tex]c(50) = 100 + 105[/tex]
[tex]c(50) =\$205[/tex]
For this sequence, write an explicit formula. Then determine the 15th term in the sequence.
1/2, 1, 3/2, 2 5/2, 3 7/2
((help ;;-;;))
Answer:
Step-by-step explanation:
[tex]S = 1/2, 1, 3/2, 4, 5/2, 3, 7/2...\\a_n = \frac{n}{2}\\a_{15} = \frac{15}{2}[/tex]
what is the height of the support beam?
Answer:
36 meters
Step-by-step explanation:
Using pythagorean theorem, 36² - 15² = 1296. √1296 = 36 meters
Answer:D. 36 m
Step-by-step explanation: Use the Pythagorean Theorem, which is a^2 + b^2 = c^2 to find the missing side. C is the hypotenuse. Plug in the numbers.
15^2 + b^2 = 39^2
Simplify.
225 + b^2 = 1521
Subtract 225 from each side.
b^2 = 1296
Square root each side to isolate b.
b = 36
The height of the support beam is 36 m.
lina puts $300 in a college fund account that gives 10% simple interest annually. How much interest would she have after 4 years?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$300\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &4 \end{cases} \\\\\\ I=(300)(0.10)(4)\implies I=120[/tex]
sin2x= ____.
a. 1/2(cos(a-b)-cos(a+b))
b. 2 sin x cos x
c. 1-2 sin^2 x
d. 2 sin x +2 cos x
The correct answer is c. 1-2 sin^2 x.
Explanation:The correct answer is c. 1-2 sin^2 x.
To find the value of sin 2x, we can use the double angle formula for sine, which states that sin 2x = 2sin x cos x. Therefore, b. 2 sin x cos x is the correct answer choice.
Correct option is (b) 2sinxcosx
Now using the trigonometric identity of 'sin(a+b)' we can find out the value of sin2x
sin (a + b) = sin a cos b + sin b cos a,
where 'a' and 'b' are angles
let 'a'='x' and 'b'='x'
[tex]sin2x=sin(x+x)\\sin2x=sinx*cosx+sinx*cosx\\sin2x=2sinxcosx[/tex]
Thus 2sinxcosx is the required answer
Write an expression to represent:
One minus the product of four and a number x
Answer:
1-4x
Step-by-step explanation:
Answer:
1 - 4xStep-by-step explanation:
The product of four and a number x: 4 · x = 4x
One minus the product of four and a number x: 1 - 4x
Which of the following equations is equivalent to 1/4x - 1/2y = 8?
(A) 2x - 4y = 8
(B) 2x - 4y = 64
(C) 4x - 2y = 64
Answer:C
Step-by-step explanation:4x _2y =64 because 8×8= 64
For this case we must find an equation equivalent to:
[tex]\frac {1} {4} x- \frac {1} {2} y = 8[/tex]
We add [tex]\frac {1} {2}[/tex] and on both sides of the equation:
[tex]\frac {1} {4} x = 8 + \frac {1} {2}y[/tex]
We multiply by 4 on both sides of the equation:
[tex]x = 32 + \frac {4} {2}y\\x = 32 + 2y[/tex]
Multiplying by 2 on both sides of the equation:
[tex]2x = 64 + 4y\\2x-4y = 64[/tex]
Answer:
Option B
Using the distance formula , find the distance from the center of your habitat to the point (x, y). Write this equation. Your answer will contain x- and y-terms.
Answer:
See explanation
Step-by-step explanation:
The distance formula is given by:
[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]
We want to find the distance between (a,b) and (x,y).
The center of the habitat is missing in the question.
Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:
[tex] d = \sqrt{(x - a)^{2} + {(y - b)}^{2} } [/tex]
For instance if the center of your habitat us (2,-1), then
[tex]d = \sqrt{(x - 2)^{2} + {(y + 1)}^{2} } [/tex]
TW¯¯¯¯¯¯¯¯¯=14.6, CW¯¯¯¯¯¯¯¯¯=6, TU¯¯¯¯¯¯¯=21.2. Find the value of VW¯¯¯¯¯¯¯¯¯.
A. 6.9
B. 8.2
C. 7.5
D. 16.1
TW x WU = CW x VW
Fill in the known values:
WU = TU - TW = 21.2 - 14.6 = 6.6
14.6 x 6.6 = 6 x VW
Simplify:
96.36 = 6VW
Divide both sides by 6:
VW = 96.36 / 6
VW = 16.06
Round to one decimal place:
VW = 16.1
The answer is D>
Answer:
D.) 16.1
Step-by-step explanation:
I got it correct on founders edtell
Pleaseeeeeeee helppppp ASAP help....
Answer:
42.5 %
Step-by-step explanation:
You would multiply the probability of the couple having a girl and the test predicting it’s a girl.
0.85 x 0.5= 0.425 = 42.5%
What is the equation?
to get the equation of a straight line, all we need is two points, hmmm say this line runs over (0 , -2) and (3 , 0), so let's use those.
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-0}{0-3}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{2}{3}(x-3)\implies y=\cfrac{2}{3}x-2[/tex]
Find the number of pages when the minutes equals 72 according to the table below. To help, write a rule relating the minutes, x, to the number of pages.
minutes: 6 15 27 72
pages: 20 50 90 ?
Answer:
240
Step-by-step explanation:
Where P = pages and x = minutes, your rule is as follows:
[tex]P=\frac{10}{3} x[/tex]
Simply plug in your last minute value to find your last page value.
[tex]P=\frac{10}{3} (72)\\P=240[/tex]
Which of the following expresses 2.4 as a fraction in simplest form ?
Answer:
its 2 4/9
Step-by-step explanation:
because i did trial and error, i converted all the fractions into decimals until one of the conversions was equal to 2.444444444444...infinite
[tex]2 \frac{4}{9}[/tex] would be the correct answer.
This is not 2.4. This is "2.44444..." because of the line over the 4 after the decimal place (this applies for any decimal such as [tex]2.48\overline{47} = 2.484747474747...[/tex]).
In general, the over-lined part can be written as a fraction of 9 (99, 999, 9999, etc. if the over-lined part has more than one digit, in increasing order of digits), which is why [tex]2 \frac{4}{9}[/tex] is the correct answer.
What are the dimensions of a rectangular box with a volume of 50b 3 + 75b2 - 2b - 3?
Answer:
[tex]\large\boxed{(2b+3)\times(5b-1)\times(5b+1)}[/tex]
Step-by-step explanation:
The formula of a volume of a rectangular box:
[tex]V=lwh[/tex]
l - lenght
w - width
h - height
[tex]V=50b^3+75b^2-2b-3=25b^2(2b+3)-1(2b+3)\\\\=(2b+3)(25b^2-1)=(2b+3)(5^2b^2-1^2)\\\\=(2b+3)\bigg((5b)^2-1^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2b+3)(5b-1)(5b+1)[/tex]
Therefore the dinemsions of thisp prism are:
[tex](2b+3)\times(5b-1)\times(5b+1)[/tex]
Answer:
the one with ++-
Step-by-step explanation:
Simplify the expression. 21 + 49 ÷ 7 + 1
Answer:
29
Step-by-step explanation:
Simplify the following:
21 + 49/7 + 1
Hint: | Reduce 49/7 to lowest terms. Start by finding the GCD of 49 and 7.
The gcd of 49 and 7 is 7, so 49/7 = (7×7)/(7×1) = 7/7×7 = 7:
21 + 7 + 1
Hint: | Evaluate 21 + 7 + 1 using long addition.
| 2 | 1
| | 7
+ | | 1
| 2 | 9:
Answer: 29