Find the quotient.

7/8 ÷ 2 1/4
WILL GIVE 30 POINTS ​

The rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.

Volume is defined as the space occupied by a three dimensional figure.

It is given that

A cube's edge lengths are each 5 inches

A rectangular prism's length and width are also 5 inches, but its height is [tex]\rm 7\dfrac{1}{2}[/tex]

The volume of the cube is given by side * side * side

Volume of cube = 5 *5 * 5 = 125 cu. inches

The volume of cuboid = length * width * height

Volume of Cuboid = 187.5 cu.inches.

Therefore the rectangular prism is 187.5 - 125 = 62.5 cu.inches greater than the volume of cube.

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Answer:

3.375 °C

Step-by-step explanation:

Mean temperature for first 7 days = 4 °C

⇒ Total temperature over first 7 days = 4 °C × 7 = 28 °C

Temperature on 8th day = -1 °C

[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]

Therefore, mean temperature for first 8 days:

= [28 - 1] ÷ 8

= 27 ÷ 8

= 3.375 °C

Answer: R62,500

Step-by-step explanation:

To find the discount, simply multiply 12.5% (0.125 in decimal form) with 500,000

500,000 x 0.125 = 62,500

Answer:

  ₹62,50

Step-by-step explanation:

The amount of discount is found by multiplying the discount rate by the amount being discounted.

  discount = 0,125 × ₹500,00 = ₹62,50

You will receive a discount of ₹62,50.

_____

Additional comment

Here, a comma is used to separate the units part of the number from the fractional part of the number. This decimal separator is an alternative to the use of a period or centered dot (·) for that purpose.

Answer:

She would have received $5.49 change

Answer:

$5.49 ~$5.50

Explanation: $20 - $15.51 = $5.49 therefore you have to round off which would initially equal to $5.50

Answer:

[tex]format \: examples \: )[/tex]

(30-30) = 40 RIGHT THE SIMILAR FROM 60 -40 AND CALCULATE ALL OF IT +4

ANSWER: 405

Answer:

width = 10 m

length = 16 m

Step-by-step explanation:

Formula

[tex]\textsf{Area of a rectangle} = wl[/tex]

[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]

(where  [tex]w[/tex] is width and [tex]l[/tex] is length)

Given:

Substituting the given values into the formulae to create two equations:

[tex]\textsf{Equation 1}: \quad wl=160[/tex]

[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]

Rearranging Equation 1 to make w the subject:

[tex]\implies w=\dfrac{160}{l}[/tex]

Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:

[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]

[tex]\implies \dfrac{160}{l}+l=26[/tex]

[tex]\implies 160+l^2=26l[/tex]

[tex]\implies l^2-26l+160=0[/tex]

[tex]\implies l^2-10l-16l+160=0[/tex]

[tex]\implies l(l-10)-16(l-10)=0[/tex]

[tex]\implies (l-10)(l-16)=0[/tex]

[tex]\implies l=10, 16[/tex]

According to Equation 1:

As width < length, the dimensions of the shop are:

Answer:

line it, then try to add each number going from the top, my mother gave me that advice before, it works (:

Step-by-step explanation:

Answer:

X go's first then Y

Step-by-step explanation:

I did this before and got 100% promise and mark me brainiest

Step-by-step explanation:

a = hours at job A

b = hours at job B

a + b = 24

a = 24 - b

5.8a + 7.4b = 158.4

note we can use the a = 24 - b identity in the second equation :

5.8×(24 - b) + 7.4b = 158.4

139.2 - 5.8b + 7.4b = 158.4

1.6b = 19.2

b = 12 hours

a = 24 - b = 24 - 12 = 12 hours

she worked 12 hours on job A and 12 hours on job B.

Answer:

67 m/s

Step-by-step explanation:

Formula for range :

Solving with the given values :

Answer:

[tex]\sf u=67\:ms^{-1}[/tex]

Step-by-step explanation:

Assuming the distance traveled is the horizontal distance.

Horizontal Range Formula

[tex]\sf R=\dfrac{u^2 \sin 2\theta}{g}[/tex]

where:

Given:

Substituting the given values into the formula and solving for u:

[tex]\implies \sf 400=\dfrac{u^2 \sin 60^{\circ}}{9.8}[/tex]

[tex]\implies \sf 3920=u^2 \sin 60^{\circ}[/tex]

[tex]\implies \sf 3920=\left(\dfrac{\sqrt{3}}{2}\right)u^2[/tex]

[tex]\implies \sf u^2=\dfrac{7840}{\sqrt{3}}[/tex]

[tex]\implies \sf u=\sqrt{\left(\dfrac{7840}{\sqrt{3}} \right) }[/tex]

[tex]\implies \sf u=67.2787196...[/tex]

[tex]\implies \sf u=67\:ms^{-1}\:(nearest\:whole\:number)[/tex]

The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭

The representation of complex number in polar form is expressed as;

y = r(cosФ + isinФ)

where;

r is the modulus

Ф is the argument

Given the vector t = –5i + 12j, the modulus of the vector is given as;

r = √(-5)²+(12)²

r = √25 + 144

r = √169

r = 13

Determine the angle between the vectors

Ф = arctan(-12/5)

Ф = -67.38

Since tan is negative in the second quadrant, hence;

Ф = 180 - 67.38

Ф = 112.62°

The representation of the vector in trigonometry form is t = 13 ❬cos 112.62°, sin 112.62°❭

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Step-by-step explanation:

[tex]5 = {a}^{x} [/tex]

[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]

[tex] \frac{5}{a} = {a}^{x - 1} [/tex]

The arrangement of the rose plants on the triangular plot is such that they

form a series or progression that is defined.

The number of rows on Bill's plot is; 8 rows

The given parameters for the triangular plot are;

Number of plants at the corner = 1 plant

Number of additional plants per row = 6 plants

Number of rose plants = 150 rose plants

The number of rows in the plot.

The difference between successive rows, d = 6

The number rose at the top vertex, a = 1

Therefore, the rose in the garden forms an arithmetic progression

The first term, a = 1

The common difference, d = 6

The number of rows Bill's plot will have, n is given by the sum of n in terms of

an arithmetic progression, Sn, is given as follows;

[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]

When Sn = 150, we get;

[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]

150 = 3·n² - 2·n

3·n² - 2·n - 150 = 0

Taking only the positive solution for n, we have;

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]

[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]

The number of rows Bill's plot has, n ≈ 7.3965

Given that the 7th row is completed, an 8th row will be present on Bill's plot

The number of rows Bill's plot will have = 8 rows

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The linear function that has a different rate of change from y = -3x+4 is A, a function with a y-intercept of -4 that passes through the point (-3,-13)

An intercept is the point where a straight line or a curve meets with the x or y axes.

Analysis:

The rate of change is the same as slope. The slope of y = -3x + 4 is -3,

All other functions Except A have a slope of -3.

for linear function A,

if y = mx + c, c = -4, x = -3, y = -13

-13= -3m - 4

-3m = -9

m = 3

In conclusion, linear function A with a y-intercept of -4 passing through the point (-3,-13) has a different rate of change from y = -3x + 4

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The domain of the function is all real numbers, the range of a function is y ≤ 4

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = –(x + 6)(x + 2)

If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.

Here the no other details are given.

But we can say:

Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4

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Answer:

2.5 kilometers

Step-by-step explanation:

One kilometer is 1000 meters

To convert from metres to kilometers, we divide by 1000

2500 ÷ 1000 = 2.5km

Answer:

x = 28

Step-by-step explanation:

By Triangle Proportionality Theorem,
14/x = 21/42
14 * 42/21 = x
x = 28

Answer:

a = -3

b = 9

c = -3

Step-by-step explanation:

[tex]a. (2^{5} )(2)^{-8} =2^{a} \\2^{(5-8)} =2^{a} \\2^{-3}=2^{a}[/tex]

[tex]a=-3[/tex]

[tex]b.\frac{4^{7} }{4^{-2} } =4^{b} \\4^{(7-(-2))} } =4^{b} \\4^{(7+2)} =4^{b}[/tex]

[tex]4^{9} =4^{b}[/tex]

[tex]b=9[/tex]

[tex]c. \frac{7^{9} }{7^{c} } =7^{12}[/tex]

[tex]7^{9-c} =7^{12}[/tex]

[tex]9-c=12[/tex]

[tex]c=9-12[/tex]

[tex]c=-3[/tex]

Hope this helps

Answer:

V =113.09734

Step-by-step explanation:

[tex]V=\pi r^{2}[/tex]

[tex]= 2^{2}[/tex] x 9= 113.09734

(which you can technically round to 1)

=113.1

Answer:

Step-by-step explanation:

Solution

The distributive property is one of the handiest tools when factoring. You can't use it all the time, but it makes this problem so much easier. Use the distributive property to factor out the 2 from all three terms.

2(x^2 - 4x - 5)

Notice how much easier the problem got. There are only 2 integers that divide into 5. One of them is 5 and the other is one. So the solution is going to look like this

2(x    5) (x    1)

But what do you put in the space? Your choice is between a plus or a minus. Look to the middle term to find out. It is a minus 4. That means that the 5 must be minus because 5 is bigger than 1.

2(x - 5)(x     1 )

So what about the second bracket? It has to be plus. An odd number of minus signs always gives a minus. We used up the one minus we had so the one must have a plus in front of it.

2(x - 5)(x  +   1 )

[tex]\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550[/tex]

[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]

Answer:

huhh

Step-by-step explanation:

Step-by-step explanation:

We know that the area of an equilateral triangle of side a cm is

Let a cm here be 9√3 then we could get our solution.

[tex] \rm\implies \rm 9 \sqrt{3} = \cfrac{ \sqrt{3} }{4} \: a {}^{2} [/tex]

[tex] \implies \rm \: \cfrac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3} [/tex]

[tex] \implies \rm \: a {}^{2} = 36[/tex]

[tex] \implies \rm \: a = \sqrt{36} = \sqrt{6 \times 6} [/tex]

[tex] \implies \rm \: a = 6 \: cm[/tex]

Thus, the side of the equilateral triangle is 6 cm.

The question is incomplete because it was not properly and correctly arranged

Complete Question:

A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m³. What is the width? A prism has a length of 7 meters, width of w, and height of 5 meters.

Which steps are correct? Check all that apply.

a) Substitute the known values into the formula: 140 = 7(w)(5).

b) Substitute the known values into the formula: 7 = 140(w)(5).

c) Substitute the known values into the formula: 5 = 7(w)(140).

d) Solve for the unknown: w = 4 m.

e) Solve for the unknown: w = 7 m.

f) Solve for the unknown: w = 2 m.

Answer:

a) Substitute the known values into the formula: 140 = 7(w)(5).

d) Solve for the unknown: w = 4 m.

Step-by-step explanation:

The steps that are correct are Options a) and d). This is because:

Step 1

The volume of a rectangular prism is calculated as:

Volume of a rectangular prism = Length (l) × Width(w) × Height(h)

The unit of the volume or a rectangular prism is in cubic metres (m³)

In the question, we are asked to find the unknown value which is the width and we were given the following known values:

Length = 7 m,

Height = 5 m

Volume = 140 m³

Step 2

Solve for the unknown value( Width)

Volume of a rectangular prism = Length (L) × Width(W) × Height(H)

140m³ = 7m × Width(m) × 5m

140m³ = 35m² × Width(m)

Width(w) = 140m³ ÷ 35m²

Width(w) = 4m

Hence, the unknown Width(w) = 4m

From the above explanation we can see that the correct steps is Option a) and Option d)

Answer:

Step-by-step explanation:

Volume of rectangular prism= Length x width x height

V=L x W x H

140=7 x W x 5

140= 35 x w

W= 140/35

W= 4

Answer:

f(x) = -1/2x + 1

Step-by-step explanation:

y intercept is +1

For slope, used points on the graph (2,0) and (0,1)

m= y2-y1/x2-x1

= (1-0)/(0-2)

= -1/2

to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.

[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]

[tex]\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-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]

The area of the circle inside the square shape is 200.96 cm²

The length of the square is given as:

L = 16 cm

This represents the diamater (d) of the circle.

The area of the circle is then calculated as:

Area = π(d/2)²

This gives

Area = 3.14 * (16/2)²

Evaluate

Area = 200.96

Hence, the area of the circle is 200.96 cm²

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Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264

Answer:

D.

Step-by-step explanation:

Use Quadratic formula

x =  [-b +- sqrt (b^2 - 4ac) ]  / 2a     with a = 6   b = -24    c = 1

  to find

         x = 2 ± sqrt (23/6)

Answer: