How many cubes with side lengths of 1/4 does it take to fill the prism?​

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{\frac{7}{3}}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{\frac{1}{3}}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{\left( \frac{1}{3}-\frac{7}{3} \right)^2+(-1-2)^2}\implies d=\sqrt{\left( -\frac{6}{3} \right)^2+(-3)^2} \\\\\\ d=\sqrt{(-2)^2+(-3)^2}\implies d=\sqrt{4+9}\implies d=\sqrt{13}[/tex]

The distance between the given coordinate points is √13 units.

The given coordinate points are (7/3,2) and (1/3,-1).

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x1, y1) and (x2, y2) is Distance = √[(x2-x1)²+(y2-y1)²].

Substitute (x1, y1)=(7/3,2) and (x2, y2)=(1/3,-1) in distance formula, we get

Distance = √[(1/3-7/3)²+(-1-2)²]

= √[(-2)²+(-3)²]

= √13 units

Therefore, the distance between the given coordinate points is √13 units.

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ANSWER

{x|x>-12 or x<12}

EXPLANATION

The given inequality is

[tex] |x| \: < \: 12[/tex]

This implies that

[tex] - x \: < \: 12 \: or \: x \: < \: 12[/tex]

Divide the first inequality by -1 and reverse the sign to get;

[tex] x \: > \: - 12 \: or \: x \: < \: 12[/tex]

The correct answer is

{x|x>-12 or x<12}

Step-by-step explanation:

the answers are in the picture

Answer:

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

Step-by-step explanation:

We are given the following expression which we are to solve for x and give the answer in a mixed form of fraction:

[tex] \frac { 3 x } { 2 } = 5 [/tex]

Taking the denominator to the other side of the equation and multiplying it to get:

[tex]3x=10[/tex]

[tex] x = \frac { 1 0 } { 3 } [/tex]

Writing it in mixed number:

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

Final answer:

To solve the equation 3x/2 = 5, first multiply both sides by 2 and then divide by 3, resulting in x = 10/3, which is 3 1/3 as a mixed number.

Explanation:

To solve the equation given, 3x/2 = 5, one must isolate the variable x. This can be done by multiplying both sides by the denominator to cancel it out, followed by dividing by the coefficient of x. Here's the step-by-step calculation:

Multiply both sides by 2 to get rid of the fraction: 2 * (3x/2) = 2 * 5, which simplifies to 3x = 10.

Divide both sides by 3 to solve for x: 3x / 3 = 10 / 3, which simplifies to x = 10 / 3.

Express 10/3 as a mixed number: 10/3 is 3 1/3 because 3 goes into 10 three times with a remainder of 1.

This gives us the final answer in terms of a mixed number.

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

We know that percent's are always taken out of the 100. This means that one proportion will have x (the unknown percent) as the part and 100 as the whole

We want to know out of what percent is 48 in the number 80. This means 48 is the part and  80 is the whole.

[tex]\frac{48}{80} =\frac{x}{100}[/tex]

Now you must cross multiply

48*100 = 80*x

4800 = 80x

To isolate x divide 80to both sides

4800/80 = 80x/80

60 = x

This means that 48 is 60% of 80

Hope this helped!

~Just a girl in love with Shawn Mendes

To find the percentage of 48 in relation to 80, dividing 48 by 80 and multiplying the result by 100 yields the answer of 60%, indicating that 48 is 60% of 80.

A percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It represents a proportion or relative amount in relation to the whole.

The term "percentage" is derived from the Latin words "per centum," which means "per hundred." It is denoted by the symbol "%".

For example, if you say "50 percent," it means "50 out of 100" or "half." It is a way of expressing a quantity or value relative to the whole, where the whole is represented as 100%.

Percentages are commonly used to compare proportions, express ratios, indicate changes, and analyze data. They are widely used in various fields such as mathematics, finance, statistics, science, and everyday life to convey relative information and make comparisons easier.

To find what percent 48 is of 80, you can follow these steps:

Divide 48 by 80:

48/80 = 0.6

Multiply the result by 100 to convert it to a percentage:

0.6 * 100 = 60

Therefore, 48 is 60% of 80.

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Answer:

24

Step-by-step explanation:

To solve the equation, multiply 60 by 2/5.

[Note: 60 can be written as 60/1]

60/1 x 2/5

Multiply the numerators:

60 x 2 = 120

Multiply the denominators:

1 x 5 = 5

Now simplify:

120/5 = 24

So, the correct answer is 24. I hope this helps! :)

Answer:

Step-by-step explanation:

Givens

To find the number of containers that can be filled with 60 founds, we can use the following expression

[tex]\frac{2}{5} c=60[/tex]

Where [tex]c[/tex] is containers. Solving for [tex]c[/tex]

[tex]c=\frac{60(5)}{2}\\ c=\frac{300}{2}\\ c=150[/tex]

Therefore, 150 containers can be filled with 60 pounds of blueberries.

Answer:

D 2<x

Step-by-step explanation:

The circle is open and the arrow goes to the right so its greater then. The circle is on 2. The answer is D 2<x

Answer:

50.27 units²

Step-by-step explanation:²

The standard equation of a circle with center at the origin is x² + y² = r², where r is the radius.  Substituting 4 for x and 0 for y yields 4² + 0² = r², so we see immediately that r = 4 units.

The formula for the area of a circle is A = πr².

Here, with r = 4, the area is A = π(4 units)² = 16π units², or

50.27 units² to the nearest hundredth.

Answer:

Option C is correct.

Step-by-step explanation:

Option C above the dashed line is correct option.

we will graph the inequality

6y - 3x > 9

6y > 9 +3x

y >9/6 +3x/6

y > 3/2 + x/2

The line is dashed because the values are greater and not equal.

The graph is shown in the figure attached.

Answer: Third option

Above the dashed line

Step-by-step explanation:

First we solve the inequality for the variable y.

[tex]6y - 3x > 9[/tex]

[tex]6y - 3x +3x > 9 +3x[/tex]

[tex]6y> 9 +3x[/tex]

[tex]y> \frac{9}{6} +\frac{3}{6}x[/tex]

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

Notice that the line that limits the region is given by the equation

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

The region is formed by all the points that are greater than the points that are on the line [tex]y= \frac{3}{2} +\frac{1}{2}x[/tex].

Therefore the region does not include the points that are on the line, but those that are above the line. Then the line is dashed.

The answer is the third option

Answer:

Option d) 76.44 units^2

Step-by-step explanation:

The approximate area of the circle is equal to the area of one sector, multiplied by 16

The area of one sector is approximate the area of one triangle

[tex]A=\frac{1}{2}(b)(h)[/tex]

we have

[tex]b=1.95\ units[/tex]

[tex]h=4.9\ units[/tex]

substitute

[tex]A=\frac{1}{2}(1.95)(4.9)=4.7775\ units^{2}[/tex]

Multiplied the area of one sector by 16

[tex]4.7775*16=76.44\ units^{2}[/tex]

Answer:

76.44 took test

Step-by-step explanation:

Step-by-step explanation:

It is important to remember that when we graph a linear equation, we get a line and when we graph a quadratic equation, we get a parabola.

Then,  given a system of a quadratic equation and a linear equation, there are three possibles cases for the solution:

- If the line and the parabola never intersect, then there is no real solution.

- If the line just touches the parabola, then there is one real solution.

- If the line and the parabola intersect at two points, then there Two real solutions.

Then the system of a quadratic equation and a linear equation may have: no intersections points, one intersection point or two intersection points.

Answer:

One solution.

Step-by-step explanation:

To determine the number of possible solutions for a triangle with A = 113° , a = 15, and b = 8, we're going to use the law of sines which states that: "When we divide side a by the sine of angle A  it is equal to side b divided by the sine of angle B,  and also equal to side c divided by the sine of angle C".

Using the law of sines we have:

[tex]\frac{sin(A)}{a} = \frac{sin(B)}{b}[/tex]

[tex]\frac{sin(113)}{15} = \frac{sin(B)}{8}[/tex]

Solving for B, we have:

[tex]sin(B)=0.4909[/tex]

∠B = 29.4°

Therefore, the measure of the third angle is: ∠C = 37.6°

There is another angle whose sine is 0.4909 which is 180° - 29.4° = 150.6 degrees. Given that the sum of all three angles of any triangle must be equal to 180 deg, we can't have a triangle with angle B=113° and C=150.6°, because B+C>180.

Therefore, there is one triangle that satisfies the conditions.

Answer:

b on edge

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Let u = x² ( choice of variable is flexible ), then

4u² - 21u + 20 = 0 ← expressed as a quadratic

This can now be solved for u and converted back into terms of x

Answer:

refer the explanation

Step-by-step explanation:

this question can be written as

X^2=y

so,x^4=y^2

so it will be 4y^2-21y+20=0

Answer:

There are 2 solutions to this equation

[tex]x=-\frac{1}{4} +i\frac{\sqrt{19} }{4} ,x=-\frac{1}{4} -\frac{\sqrt{19} }{4}[/tex]

Step-by-step explanation:

for  a quadratic equation of the form ax^2 + bx + c = 0 the solutions are

[tex]x_{1,2}=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x=\frac{-2+\sqrt{2^{2}-4.4.5 } }{2.4} :-\frac{1}{4}+ i\frac{\sqrt{19} }{4} \\x=\frac{-2-\sqrt{2^{2}-4.4.5 } }{2.4} :-\frac{1}{4} -i\frac{\sqrt{19} }{4}[/tex]

brainiest plz

Answer: Second Option

[tex]g(x) = 2x^2 + 1[/tex]

Step-by-step explanation:

By definition, a function f(x) is an even function if:

[tex]f (-x) = f (x)[/tex]

This means that each input value x and its negative -x are assigned the same output value y.

To verify which of the functions is even, you must test [tex]f(-x) = f(x)[/tex] for each of them

First option

[tex]g(x) = (x - 1)^2 + 1[/tex]

[tex]g(-x) = (-x -1)^2 +1\\\\g(-x) = ((-1)(x+1))^2 +1\\\\g(-x) = (-1)^2(x+1)^2 +1\\\\g(-x) = (x+1)^2 +1\neq g(x)[/tex]

Second option

[tex]g(x) = 2x^2 + 1[/tex]

[tex]g(-x) = 2(-x)^2 + 1[/tex]

[tex]g(-x) = 2x^2 + 1=g(x)[/tex]

Third option

[tex]g(x) = 4x + 2[/tex]

[tex]g(-x) = 4(-x) + 2[/tex]

[tex]g(-x) = -4x + 2\neq g(x)[/tex]

Fourth option

[tex]g(x) = 2^x[/tex]

[tex]g(-x) = 2^(-x)[/tex]

[tex]g(-x) = \frac{1}{2^x}\neq g(x)[/tex]

Answer:

B

Step-by-step explanation:

Just took test on edge

Answer:

your answer is C

Step-by-step explanation:

vertices neither contain angle nor contain complement

Answer:

C. P, Q and R.

Step-by-step explanation:

In geometry to express verticles, we use only the capital letter for that point.

It's not A because that's the symbol to represent angles.

It's not B because of the right answer in into the options.

it's not D because having both capital letters with the lines above means the line between those points.

The correct answer is C.

Final answer:

To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, use the formula A = P(1 + r/n)^(nt). The balance after 5 years will be $13,933.16.

Explanation:

To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, you can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal is $10,000, the annual interest rate is 6.92%, and n is 1 (compounded annually), and t is 5 years.

Calculate (1 + r/n)^(nt): (1 + 0.0692/1)^(1 * 5) = 1.0692^5 = 1.39331595

Calculate the final amount using the formula: A = 10,000 * 1.39331595 = $13,933.16

Therefore, the balance after 5 years will be $13,933.16.

Answer:

-6x^4-8x^2 or -2x^2(3x^2+4)

Step-by-step explanation:

Given expression is:

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

In order to write the expression in simplest form we have to multiply the terms which needs to be multiplied.

So,

[tex]= -10x^4-8x^2+4x^4[/tex]

Combining alike terms

[tex]= -10x^4+4x^4-8x^2\\=-6x^4-8x^2\\[/tex]

Can also be written as:

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

Answer:

-2x^2(3x^2 + 4).

Step-by-step explanation:

2x^2(-5x^2 - 4) + 4x^4

Distribute the 2x^2 over the parentheses:

= -10x^4 - 8x^2 + 4x^4

= - 6x^4 - 8x^2

=  -2x^2(3x^2 + 4).

Answer:

1.74 %

Step-by-step explanation:

the equivalent monthly interest rate of a credit card with an annual interest rate of 23% is 1.74 %.

Hope this helps!

[tex]\bf \cfrac{1}{1-sin(x)}+\cfrac{1}{1+sin(x)}=\cfrac{2}{cos^2(x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the LCD of [1-sin(x)][1+sin(x)]}}{\cfrac{[1+sin(x)]1~~+~~[1-sin(x)]1}{\underset{\textit{difference of squares}}{[1-sin(x)][1+sin(x)]}}} \\\\\\ \cfrac{1+sin(x)+1-sin(x)}{1^2-sin^2(x)}\implies \cfrac{1+sin(x)+1-sin(x)}{1-sin^2(x)}[/tex]

recall that 1 - sin²(θ) = cos²(θ).

Answer:

AC ≈ 12.9 cm

Step-by-step explanation:

Using the ratio

sin40° = [tex]\frac{b}{20}[/tex]

Multiply both sides by 20

20 × sin40° = b, hence

AC = b = 20 × sin40° ≈ 12.9

Answer:

Last graph on the right.

Step-by-step explanation:

Try substituting some values for x and see which graph is valid.

when x = 0, y = f(0) = 3 [tex](2/3)^{0}[/tex] = 3 (1) = 3

When we compare this to the graphs, we immediately see that the first 2 are not correct because in those cases, when x=0, y = 6 (i.e not 3).

Next we try  x = 1

when x = 1, y = f(1) = 3 [tex](2/3)^{1}[/tex] = 3 ([tex]\frac{2}{3}[/tex]) = 2

Comparing the graphs ones again, show that only the last graph has x=1 and y = 2.

Answer:

D

Step-by-step explanation:

Answer:

11/4

Step-by-step explanation:

ok lets say one 2 is equal to 4/4  so you have 8/4 plus the 3/4

Answer:

11/4

Step-by-step explanation:

you have to multiply 2 by 4 because there are 2 groups of four which would get you to 8 then add the left overs which would make it 11 and bam 11/4

Answer:

B. 48

Step-by-step explanation:

Use the property of secant and tangent to the circle: If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

In yuor case,

Tangent = x

External secant = 6

Secant =6+2

So

[tex]x^2 =6\cdot (2+6)\\ \\x^2 =6\cdot 8\\ \\x^2 =48[/tex]

Answer:

It's literally 16

Step-by-step explanation:

Just 16 bro

Answer:

If the roots of an equation are x = -1 ± i, it means that the factorized form of that equation is: (x + 1 + i)(x+ 1 - i) = 0.

Using the distributive property, we have:

(x + 1 + i)(x+ 1 - i) = x^2 + x - ix + x + 1 - i + ix + i + 1

Combining like-terms and simplifying:

⇒ x^2 + x + x + 1   + 1 = x^2 + 2x + 2 = 0

Therefore, the stament is correct. If the roots of an equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.

Answer:

equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.

Step-by-step explanation:

its correct

Answer:

all pairs are congruent

1) Congruent by SAS (Side-Angle-Side)

2) Congruent by SAS (Side-Angle-Side)

3) Congruent by HL  (Hypotenuse-leg)

Answer:

• Each pair of triangles is congruent

~You can tell that each pair is congruent for the following reasons: (1) The legs, or sides, of the triangles in both #1 & #3 are both the same number. (2) The tick marks in #2 are the same, meaning the side lengths are similar.

• Both triangles in each pair are right triangles.

• The triangle pairs in #1 & #3 are rotations, while the triangle pair for #2 is a translation.

I was unaware of any specific answers, so I hope this is helpful!!!

The answer is:

The equation of the line with slope 3 that passes through the point M(1,2) is:

[tex]y=3x-1[/tex]

To determine the equation of the line with slope equal to 3, that passes through the point M(1,2) we can use the following equation:

The slope-intercept of the line is defined by the following equation:

[tex]y=mx+b[/tex]

Where,

m is the slope of the line

b is the constant number which represents the y-axis intercept of the line.

So, using the given information, we have:

[tex]y=3x+b[/tex]

Then, using the given point to calculate "b", we have:

[tex]2=3*1+b[/tex]

[tex]2=3+b[/tex]

[tex]2-3=b[/tex]

[tex]b=-1[/tex]

So, rewriting the equation, we have:

[tex]y=3x-1[/tex]

Hence, the equation of the line with slope 3 that passes through the point M(1,2) is:

[tex]y=3x-1[/tex]

Have a nice day!

Answer:

D. alternate interior angles

Step-by-step explanation:

The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles

So p and w are alternate interior angles

Answer:

No

Step-by-step explanation: