Ivan is putting books in his bookcase. He has
already put 74 books in the bookcase but he has
225 books. How many more books does he have to
put in the bookcase?

Answer:

C

Step-by-step explanation:

proportion can be used to show that the slope of AC is equal to the slope of CG

Slope of AC = (2-0)/(3-0) = 2/3

Slope of CG = (6-2)/(9 -3) = 2/3

So answer is :

C)

      2 − 0        6 − 2

   ------------ =  -----------

      3 − 0         9 − 3

Answer:C

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

If x is the number of 1/8 yard long pieces, then the total length is x * 1/8.  We know that the total length is 3/4 yards.  Therefore:

x * 1/8 = 3/4

Divide:

x = (3/4) / (1/8)

To divide a fraction, multiply by its reciprocal:

x = (3/4) * (8/1)

x = 24/4

x = 6

She has 6 pieces.

Answer:

Adrianna will have 6 1/8 yard pieces.

Step-by-step explanation:

[tex]1/8*2/1=2/8 \\2/8=1/4\\So\\6/8=3/4[/tex]

Answer:

No triangle can be constructed with given measures.

Step-by-step explanation:

Refer the following figure.

     AB = c = 7.6 cm

     AC = b = 5.4 cm

     ∠ABC = B = 50°

Sine rule is given by [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Substituting

        [tex]\frac{5.4}{sin50}=\frac{7.6}{sinC}\\\\sinC=1.078[/tex]

Value of sinC is more than 1, which is not possible.

Hence no triangle can be constructed with given measures.

Answer:

The value of x is 4√5 ⇒ 1st answer

Step-by-step explanation:

* Lets revise the rules in the right angle triangle when we draw the

 perpendicular from the right angle to the hypotenuse

- In triangle ABC

# Angle B is a right angle

# The hypotenuse is AC

# BD ⊥ AC

∴ (AB)² = AD × AC

∴ (BC)² = CD × AC

∴ (BD)² = AD × CD

∴ BD × AC = AB × BC

* Lets use one of these rules to solve the problem

- y is the perpendicular from the right angle to the hypotenuse

- x is one leg of the right angle

∵ The length of the hypotenuse = 5 + 11 = 16 units

∵ The part nearest to x = 5

* Lets use the rule (AB)² = AD × AC

∴ x² = 5 × 16 = 80 ⇒ take √ for both sides

∴ x = √80 = 4√5 units

[tex]

\frac{\sqrt{9}}{\sqrt{81}}=\frac{3}{9}=\boxed{\frac{1}{3}}

[/tex]

The answers are A and B.

Hope this helps.

r3t40

Answer: Less than 1 bag.

Step-by-step explanation:

Take the total number of bags and divide it by them between the 12 yards.

7.5/12 is equal to 0.625 which is less than 1 bag.

Hope this helps!

Answer:

Michael will use 3/8 cup of flour.

Step-by-step explanation:

Half of a Fraction:

1.  Reduce fraction to its lowest terms.

2.  If the numerator is an even number than divide the numerator by 2.

Example:  4/5 divided in half would be 2/5.

3.  If the numerator is an odd number than multiply the denominator by 2.

Example:  1/3 divided in half would be 1/6.

3/4 cup of flour divided in half would be 3/8 because the numerator 3 is an odd number so the denominator of 4 would be multiplied by 2 equaling 8.

Hey there!

If we have two white marbles and seven purple marbles, our first probability is out of nine.

First of all, we have the probability of selecting a purple marble, 7/9.

Now, if we do not replace it, there are only eight marbles left. Therefore, getting a white marble is 2/8, or 1/4.

We multiply these probabilities together to get our answer to a.

7/9(1/4)= 7/36

a. 7/36

Now, let's do b. We have 2/9, and then 1/8, giving us 1/36.

b. 1/36

Now, let's calculate selecting two purple to help us with C.

We have 7/9, and then 6/8, or 3/4.

7/9(3/4)= 7/12

Since there is a majority of purple marbles, there is a C) greater probability of selecting two purple marbles in a row.

I hope this helps!

Answer:

A. 7:9 B. 1:4 C. Purple

Step-by-step explanation:

A. Because there are 7:9 B. Because 1:4 C. Because Purple has more

Answer:

3/5^3 = 27

125

= 0.216

Step-by-step explanation:

Power: 3

5

^ 3 = 33

53

= 27

125

Answer:

The missing image from the problem is attached

The answer is (C) Each of the lateral faces has an area of 464 square inches.

Step-by-step explanation:

Base is a square that is 32 in

The height of one of the 4 lateral faces is 29 in

-----------------------------------------------------------------

Base is L*W --> 32*32 = 1024 square inches

(1) Lateral face is 1/2*b*h = 0.5*32*29 = 464 square inches

----------------------------------------------------------------

Since the answers are about the face and/or one lateral face only, those two numbers are important. (C) is the only answer that matches

Each of the lateral faces has an area of 464 square inches , Option C is the correct answer

A square pyramid is a three dimensional figure , having square as the base and four triangular faces which meet at a single point called at a single point.

It is given in the question (figure is attached )

Base of the square pyramid is 32 in

The height of one of the 4 triangle is 29 in

Area of the base = 32* 32

= 1024 sq.in

Area of the lateral face (triangle ) =  1/2*b*h

= (1/2) * 32 * 29

= 464 sq. in

Therefore Option C is the correct answer , Each of the lateral faces has an area of 464 square inches.

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Answer:

12 gallons

Step-by-step explanation:

let x be the amount tank can hold, then

[tex]\frac{1}{3}[/tex] x + 2 = [tex]\frac{1}{2}[/tex] x

Multiply through by 6

2x + 12 = 3x ( subtract 2x from both sides )

12 = x

The tank can hold 12 gallons

Greg's gas tank can hold 12 gallons of gas. We know this because when Greg's tank is 1/3 full and he buys 2 gallons of gas it becomes 1/2 full. The difference between 1/2 and 1/3 of a tank, or 1/6 of the tank, is equal to 2 gallons.

The subject of this question is mathematics, specifically within the scope of fractions and simple algebra. The question tells us that when Greg's gas tank is 1/3 full and he adds 2 gallons, the tank becomes 1/2 full. This tells us that the difference between 1/2 and 1/3 of the tank's capacity is equal to 2 gallons. In mathematical terms, this can be represented as 1/2 - 1/3 = 2/6 - 2/6 = 1/6. Therefore, 1/6 of Greg's gas tank equals 2 gallons. If 1/6 of the tank equals 2 gallons, the entire tank (or 6/6) would hold 12 gallons of gasoline.

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Answer:

[tex]\large\boxed{\sqrt{80}=4\sqrt5}[/tex]

Step-by-step explanation:

Method 1:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (-4, 1) and (4, 5). Substitute:

[tex]d=\sqrt{(4-(-4))^2+(5-1)^2}=\sqrt{8^2+4^2}=\sqrt{64+16}=\sqrt{80}[/tex]

[tex]\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5[/tex]

Method 2:

Look at the picture.

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=8,\ leg=4,\ hypotenuse=x[/tex]

Substitute:

[tex]x^2=8^2+4^2\\\\x^2=64+16\\\\x^2=80\to x=\sqrt{80}\\\\x=4\sqrt5[/tex]

Answer:

x=−7+√130 or x=−7−√130

Step-by-step explanation:

Answer:

Step-by-step explanation:

x²+14x+17=-98

add 98 to each side

x²+14x+115=0

Solve with quadratic formula

a=1

b=14

c=115

\frac{-14 ±\sqrt{14^2-4*1*115} }{2*1}

Answer:

[tex]1.\ m<6\\2.\ g\leq-4\\3.\ y<41\\4.\ b<4\\5.\ h<-30\\6.\ x>-2\\7.\ t>9\\8.\ w<28[/tex]

Step-by-step explanation:

1. Subtract 10 from both sides. Then:

[tex]m+ 10< 16\\ m+ 10-10< 16-10\\m<6[/tex]

2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-2g\geq8\\\\\frac{-2g}{-2}\geq\frac{8}{-2}\\\\g\leq-4[/tex]

3. Add 22 to both sides. Then:

[tex]y-22< 19\\ y-22+22<19+22\\y<41[/tex]

4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-7b>-28\\\\\frac{-7b}{-7}>\frac{-28}{-7}\\\\b<4[/tex]

5. Subtract 30 from both sides. Then:

[tex]h+30<0\\ h+30-30<0-30\\h<-30[/tex]

6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:

[tex]-5x<10\\\\\frac{-5x}{-5}<\frac{10}{-5}\\\\x>-2[/tex]

7. Subtract 13 from both sides. Then:

[tex]t+13>22\\ t+13-13>22-13\\t>9[/tex]

8. Add 12 to both sides. Then:

[tex]w-12< 16\\ w-12+12<16+12\\w<28[/tex]

Answer:

Step-by-step explanation:

The formula of an area of a rectangle:

[tex]A=l\times w[/tex]

l - length

w - width

We have l = x + 12 and w = x - 5. Substitute:

[tex]A=(x+12)(x-5)[/tex]       use FOIL (a + b)(c + d) = ac + ad + bc + bd

[tex]A=(x)(x)+(x)(-5)+(12)(x)+(12)(-5)[/tex]

[tex]A=x^2-5x+12x-60[/tex]         combine like terms

[tex]A=x^2+7x-60[/tex]

[tex](2x-5)(3x^2-4x+2)[/tex]      use the distributive property a(b + c) = ab + ac

[tex]=(2x-5)(3x^2)+(2x-5)(-4x)+(2x-5)(2)\\\\=(2x)(3x^2)+(-5)(3x^2)+(2x)(-4x)+(-5)(-4x)+(2x)(2)+(-5)(2)[/tex]

[tex]=6x^3-15x^2-8x^2+20x+4x-10[/tex]       combine like terms

[tex]=6x^3+(-15x^2-8x^2)+(20x+4x)-10\\\\=6x^3-23x^2+24x-10[/tex]

Answer:

x=2

Step-by-step explanation:

Answer:

C) h(x)=[tex]4^{x-1}[/tex]

Step-by-step explanation:

Answer:

4x + y = 32

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (7, 4) and (x₂, y₂ ) = (5, 12)

m = [tex]\frac{12-4}{5-7}[/tex] = [tex]\frac{8}{-2}[/tex] = - 4, thus

y = - 4x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation.

Using (7, 4), then

4 = - 28 + c ⇒ c = 4 + 28 = 32

y = - 4x + 32 ← in slope- intercept form

Add 4x to both sides

4x + y = 32 ← in standard form

Answer:

8800

Step-by-step explanation:

a yard is equals 3 feet a mile is 5 280

Answer: 8800 yards

Step-by-step explanation:

1 mile = 1760 yards

1760 yards x 5 miles = 8800 yards

Answer: D. 0.53

Step-by-step explanation:

From the given picture, the number of persons from California and prefers brand A = 90

The total numbers of persons prefer brand A = 170

The probability that the person is from California, given that the person prefers brand A will be :-

[tex]\dfrac{\text{Persons from California and prefers brand A}}{\text{Persons prefer brand A}}\\\\=\dfrac{90}{170}=0.529411764\approx 0.53[/tex]

Hence, The probability that the person is from California, given that the person prefers brand A = 0.53

Answer:

D 0.53

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]k - \text{scale of similar}[/tex]

[tex]\text{If}\ AB\sim CD\ \text{in scale}\ k,\ \text{then}\ \dfrac{length_{AB}}{length_{CD}}=k[/tex]

[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{area_A}{area_B}=k^2[/tex]

[tex]\text{If}\ A\sim B\ \text{in scale}\ k,\ \text{then}\ \dfrac{volume_A}{volume_B}=k^3[/tex]

[tex]\text{We have}\ B\sim A\ \text{in scale}\ k=5.\ V_A=12\ m^3,\ \text{therefore}\\\\\dfrac{V_B}{V_A}=k^3\to\dfrac{V_B}{12}=5^3[/tex]

[tex]\dfrac{V_B}{12}=125[/tex]            multiply both sides by 12

[tex]V_B=1500\ m^3[/tex]

Answer:

400cm

Step-by-step explanation:

Answer:

it is 400cm2

Step-by-step explanation:

i know things

For this case we must simplify the following expression:

[tex]\sqrt {\frac {16} {25}}[/tex]

We can rewrite 16 as:[tex]2 ^ 4 = 2 * 2 * 2 * 2[/tex]

We can rewrite 25 as:[tex]5 ^ 2 = 5 * 5[/tex]

[tex]\sqrt {\frac {2 ^ 4} {5 ^ 2}} =\\\frac {\sqrt {2 ^ 4}} {\sqrt {5 ^ 2}} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression:

[tex]\frac {2 ^ 2} {5} =\\\frac {4} {5}[/tex]

Answer:

[tex]\frac {4} {5}[/tex]

Answer:

13%

Step-by-step explanation:

Please use the $ sign.

The simple interest formula is i = p*r*t, where p is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years.  Here, t = 1/4 year; r is unknown, p is $5004 and i is $162.63.

Writing this out with the given info, we get:

$162.63 = $5004*r*(1/4).

We can solve this for r by multiplying both sides by 4/$5004:

(4/$5004)($162.63)  = (4/$5004)($5004)*r*(1/4) = r

Evaluating r, we get (4)($162.63)/$5004 = 0.13

The interest rate, r, is 0.13, or 13%.

Answer:

the answer is 37.7 so the point closest to 40.

Step-by-step explanation:

Answer: the one between 30 and 40

Step-by-step explanation:

Answer:

y=-1x+5

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0-1}{5-4}\implies \cfrac{-1}{1}\implies -1 \\\\\\ \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-1=-1(x-4) \\\\\\ y-1=-x+4\implies y=-x+5[/tex]

2x^2 + 2x - 24

= 2x^2 + 8x - 6x -24

= 2x(x + 4) -6(x + 4)

= (x+4)(2x-6)

Answer:

.

Step-by-step explanation:

The trick here is to notice that all 3 terms can be div. by 2:

2(x^2 + x - 12)

Note that -12 factors into -3 * 4 or -4 * 3.  Thus,

x^2 + x - 12 = (x-4)(x+3), and so 2x2 + 2x − 24 = 2(x-4)(x+3).

Answer:

B is not necessarily true

Step-by-step explanation:

A) This is always true

B) This is not necessarily true

When two lines intersect, they form angles at the intersection as D says, but that does not mean that the angle will always be 90 degrees as is required for the two intersecting lines to be perpendicular

C) This is always true

D) This is always true

Option B) The lines are not perpendicular is not necessarily true.

When two lines intersect and following are the three different possibilities:

1) They are parallel, if lines are parallel they can never intersect.

2)They cross each at an angle and the point of intersection is unique that is they intersect at only one point.

3) Two lines coincide, that is every point on line 1 is a point on line 2.

Now

In option B it is given that lines are perpendicular that is the specific case of (2) When angle is 90°.

Therefore, it is not necessarily true.

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I know B is on possible choice for this and maybe d almost certain

c) and d)

c) 4a-6b+2c+c

d) 4a-6b+3c

Answer:

m∠4 = 111°

Step-by-step explanation:

∠4 and ∠5 are same side (interior) angles, and since lines A and B are parallel, they will be congruent.

So, m∠4 = m∠5

Substitute: m∠4 = 111°

Answer:

-4,4

Step-by-step explanation:

I just answered it on edge and got it right trust me

The coordinate of the point C' after the rotation of 360 degrees will be the same as the coordinate of C.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

Rectangle ABCD is rotated 360 around the origin.

If any object is rotated by 360 degrees about the origin. Then the position of the object does not change.

Then the coordinate of the point C' after the rotation of 360 degrees will be the same as the coordinate of C.

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