Show all work on each of the 8 problems
2.
You are building a rectangular chest. You want the length to
be 6 feet, the width to
be 2 feet, and the volume to be 24 cubic feet. What should
the height be?
ne.

No, there are three different values for x when each expression is set equal to 10.

Answer: x = 112°, z = 31°

Step-by-step explanation:

We can find the measurement of angle x since ∠x and 68° are same-side interior angles and they are supplementary.

            180° - 68° = x

            112° = x

            x = 112°

Next, we can find the measurement of angle x because of the corresponding angles and vertical angles.

            x = (4z - 12)

            112° = (4z - 12°)

            124° = 4z

            z = 31°

The value of length of segment t in the intersecting chords is determined as 6.93.

The value of length of segment t is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that the product of two segments of a chord is equal to the product of the two segments of the second intersecting chord in the circle.

From the diagram, the length of t is calculated by setting up the following equation;

4 x ( 4 + 8)  = t x t

4 (12) = t²

48 = t²

t = √ (48)

t = 6.93

Learn more about intersecting chords here: https://brainly.com/question/13950364

#SPJ1

We start by drawing a rectangle around the triangle as shown in the diagram below.

Area of RST = Area of rectangle - (area of triangle A + area of triangle B + area of triangle C)

Area of RST = (8×4) - [ (1/2×8×2) + (1/2×4×3) + (1/2×5×2) ] ⇒ we factorise the 1/2 out of the expression for the area of triangle A, B, and C

Area of RST = (8×4) - 1/2 (16+12+10), The answer is A.

MARK AS BRAINLIEST. YOU SAID THAT. THANK YOU!

Answer:

3700kg

Step-by-step explanation:

Use this idea.

"percent" means "per hundred"

Over 100% is more than what you started with.

To do math with percents, change them to a decimal.

145% is 1.45

1.45x = 5365

divide both sides by 1.45

x = 3700

The original value is calculated by dividing 5365 kg by 1.45, which gives approximately 3700 kg as the result.

To find the original value, you need to understand that 145% is equivalent to 145/100 or 1.45. This means that what we have (5365 kg) is 1.45 times the original value. So, to find the original value, we need to divide 5365 kg by 1.45.

Step 1: Convert 145% to a decimal by dividing 145 by 100 to get 1.45.

Step 2: Divide 5365 kg by 1.45.

The calculation looks like this: 5365 kg / 1.45 = 3700 kg (approximately)

So, the original value is about 3700 kg.

https://brainly.com/question/329987

#SPJ2

An equation of the circle that has center (3,5) and a diameter with length of 6 units is (x - 3)² + (y - 5)² = 3².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

Center (h, k) = (3, 5)

Radius (r) = diameter/2 = 6/2 = 3 units.

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 5)² = 3²

Read more on equation of a circle here: brainly.com/question/15626679

#SPJ1

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

Learn more about law of sines here:

https://brainly.com/question/17289163

#SPJ1

Answer:

1st question, see attachment (-32 is answer). 2nd question, answer is (x+3).

Step-by-step explanation:

please see attachment for 1st question.

2nd question:

-3 means x + 3

for any number A

(-A) is x + A

(A) is x - A

f(0) just means put 0 wherever x is in equation

Answer: The answer is D, reflection, then rotation results in an image that is congruent to the original.

Step-by-step explanation:

It is upsetting to get a question wrong and the teacher doesn't really explain the right answer. You were so close but you just needed to flip the answers rotation and reflection around.

In the first image, the two triangles ACB and EDF are symmetrically are across from each other, which is called reflection.

ACB-reflection-BCA

Then in the second image, triangle GHI is rotated 90 degrees counterclockwise, which would obviously be called rotation.

A                  

C -rotation- BCA

B

Therefore, the first step is reflection, and the second step is rotation, making the answer to this question d. Hope this helps with the clarified explanation!

-From a Fifth Grade Honors Student!

To determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle, we can compare the given information with the formulas for each law.

The Law of Sines states:

a / sin(A) = b / sin(B) = c / sin(C)

The Law of Cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are given the lengths of all three sides of the triangle (a = 6.0, b = 7.7, c = 13.6). Therefore, we have enough information to use the Law of Cosines to solve the triangle.

Using the Law of Cosines, we can find the measures of the angles:

c^2 = a^2 + b^2 - 2ab * cos(C)

(13.6)^2 = (6.0)^2 + (7.7)^2 - 2 * 6.0 * 7.7 * cos(C)

184.96 = 36 + 59.29 - 92.4 * cos(C)

184.96 = 95.29 - 92.4 * cos(C)

92.67 = -92.4 * cos(C)

cos(C) ≈ -1

Since the cosine of an angle cannot be greater than 1 or less than -1, it is not possible for the given triangle to have an angle with a cosine of -1. Therefore, the triangle is not solvable with the given side lengths.

In this case, the Law of Cosines is needed, but the triangle cannot be solved with the given information.

554 students is the required number that would have to be sampled

To determine the sample size needed to limit the margin of error in a 95% confidence interval, we can use the formula for the margin of error in a sample mean estimate:

E = z * (σ/√n)

Here, E is the desired margin of error, z is the z-score corresponding to the desired confidence level (for a 95% confidence level, z = 1.96), σ is the standard deviation, and n is the sample size. We can solve for n to find:

n = (z * σ / E)²

Substituting the given values:

n = (1.96 * 300 / 25)²

Now, calculate the value:

n = (23.52)^2 = approximately 553

Therefore, you should sample 553 students.

Read more on sample size  here:https://brainly.com/question/30647570

#SPJ1

The conditional statement is solved and the axiom of schema of separation is given

Given data ,

The Axiom Schema of Separation, often referred to as the Axiom Schema of Subset Collection, is a set theory axiom schema that enables us to create a new set out of an existing one by defining a requirement that the members of the new set must meet.

For any set A and any condition P(x), there exists a set B such that for any element x, x is an element of B if and only if x is an element of A and satisfies the condition P(x).

In other words, given a set A, we can define a new set B that consists of all elements of A that satisfy a given condition P(x).

Hence , the axiom of separation is solved

To learn more about axioms click :

https://brainly.com/question/30105557

#SPJ1

Answer:

84

Step-by-step explanation:

300 times .28 = 84.

Answer: 28% of 300 is 84

Step-by-step explanation:

Write 28% as 28/100.

Since, finding the fraction of a number is the same as multiplying the fraction with the number, we have

28/100 of 300 = 28/100 × 300 OR 0.28 x 300

When you multiply them together, you would get 84. Therefore, the answer to the following would be 84. Hope this helps!

-From a Fifth Grade Honors Student!

Hello !

Answer:

[tex]\boxed{ \sf a =3 }[/tex]

Step-by-step explanation:

We want to find the value of a that satisfies the following equation :

[tex]\sf 24 = 6(3a - 5)[/tex]

First, let's expand the right side :

[tex] \sf 24 = 6 \times 3a + 6 \times ( - 5) \\\sf 24 = 18a - 30[/tex]

Now let's add 30 to both sides of the equation :

[tex] \sf 24 + 30 = 18a - 30 + 30 \\ \sf54 = 18a[/tex]

Finally, let's divide both sides by 18 :

[tex] \sf\frac{54}{18} = \frac{18a}{18} \\ \boxed{ \sf a =3 }[/tex]

Have a nice day ;)

The z-score corresponding to a student who scored 85% in Clarice's class is 1.

To calculate the z-score for a student with a score of 85% in Clarice's class, we need to use the formula:

z = (x - μ) / σ

where:

z is the z-score

x is the individual student's score

μ is the mean score

σ is the standard deviation

Given:

x = 85% (the student's score)

μ = 75% (mean score)

σ = 10% (standard deviation)

Plugging in these values into the formula, we get:

z = (85% - 75%) / 10%

Simplifying the equation:

z = 10% / 10%

z = 1

Therefore, the z-score corresponding to a student who scored 85% in Clarice's class is 1.

for such more question on z-score

https://brainly.com/question/15222372

#SPJ11

Step-by-step explanation:

They are chords that cover the same arc length, so the chords are =

2s = s + 11     subtract 's' from both sides of the equation

s = 11

The equation of the tangent line at (0, 2) to the circle is 2x + 3y = 6.

We have,

To find the equation of the tangent at the point (0, 2) to the circle with equation (x + 2)² + (y + 1)² = 13,

We can use the following steps:

- Find the slope of the tangent line:

The slope of the tangent line at a point on the circle is equal to the negative reciprocal of the slope of the radius passing through that point. Since the center of the circle is at (-2, -1) and the point of tangency is

(0, 2), the slope of the radius passing through the point of tangency can be calculated as:

The slope of radius = [tex](y_2 - y_1) / (x_2 - x_1)[/tex] = (2 - (-1)) / (0 - (-2)) = 3/2.

Using the point-slope form:

[tex]y - y_1 = m(x - x_1),[/tex] where [tex](x_1, y_1)[/tex] is the point of tangency and m is the slope, we can substitute the values of [tex](x_1, y_1)[/tex] = (0, 2) and m = -2/3 into the equation:

y - 2 = (-2/3)(x - 0)

Simplifying the equation:

y - 2 = -2/3x

Multiplying both sides by 3 to eliminate the fraction:

3y - 6 = -2x

Rearranging the equation to the standard form:

2x + 3y = 6.

Therefore,

The equation of the tangent line at (0, 2) to the circle is 2x + 3y = 6.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The experimental probability of the computer generating a 3 or a 4 will be 28%.

Experimental probability can be found in the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event;

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

We are given that a computer generates 75 integers from 1 to 8 at random. The results are recorded in this table.

Outcome;

1 2 3 4 5 6 7 8

Number of times outcome occurred;

12 16 9 12 4 7 5 10

Therefore,

P_e(E) = 9 + 12 /2

P_e(E) =28%

Learn more about experimental probability here:

https://brainly.com/question/2547434

#SPJ1

Answer:28%

Step-by-step explanation:
i took the quiz<33

Answer:

C

Step-by-step explanation:

First it is a reflection of the original then a fractional dilation that makes the reflection SMALLER...it is no longer CONGRUENT, but it is SIMILAR

Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

Answer:

y = - [tex]\frac{4}{5}[/tex] x - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

here m = - [tex]\frac{4}{5}[/tex] and y - intercept = (0, - 4 ) ⇒ c = - 4

y = - [tex]\frac{4}{5}[/tex] x - 4 ← equation of line

Answer: 12^2

Step-by-step explanation:

The formula for the Pythagorean Theorem is a^2+b^2=c^2

We are given a & c.

9^2 + b^2 = 12^2

12^2 = 255

9^2 = 81

225 - 81 = 144

[tex]\sqrt{144}[/tex] = 12

Therefore 12^2 is your correct answer.

The statement is proved: PX = 12√6/5 and PY = 12√6/7.

To prove that PX = 12√6/5 and PY = 12√6/7, we will use the properties of similar triangles and the Pythagorean theorem.

First, let's denote the intersection point of the diagonals as O.  

We know that triangle ABP is similar to triangle CDP, as they share the same angles due to being vertical angles.

Therefore, we can write the following proportion:

AB/CD = BP/PD

Substituting the given values, we have:

6/12 = BP/PD

Simplifying, we find:

BP = PD/2

Since CP/PD = 1, we can conclude that CP = PD.

Now, let's consider triangle ABP and triangle CBO.

These triangles are similar because they share the same angles (due to being vertical angles) and have proportional sides.

We can write the following proportion:

AB/BC = BP/CO

Substituting the given values, we have:

6/7 = BP/CO

Rearranging the equation, we find:

CO = (7/6)BP

Now, let's focus on triangle ODP.

Using the Pythagorean theorem, we can write the following equation:

[tex]OD^2 = OP^2 + PD^2[/tex]

Since we want to find PX and PY, which are the altitudes from P to AD and BC respectively, we need to express OP in terms of PX and PD, and OD in terms of PY and PD.

Looking at triangle ODP, we can see that OP = PX + OX and OD = PY + OY.

Substituting these expressions into the Pythagorean theorem equation, we have:

[tex](PX + OX)^2 = OP^2 = (PY + OY)^2 + PD^2[/tex]

Expanding and simplifying the equation, we get:

[tex]PX^2 + 2PXOX + OX^2 = PY^2 + 2PYOY + OY^2 + PD^2[/tex]

Since OX = OY = 0 (the altitudes are perpendicular to the bases), the equation simplifies to:

[tex]PX^2 = PY^2 + PD^2[/tex]

Now, let's substitute the given values into this equation:

[tex](PX)^2 = (12\sqrt{6/7} )^2 + (PD)^2[/tex]

Simplifying further, we get:

[tex](PX)^2 = 72/7 + (PD)^2[/tex]

We know that PD = CP = CD - CP = 12 - PD, so we substitute this expression into the equation:

[tex](PX)^2 = 72/7 + (12 - PD)^2[/tex]

Now, we can solve for [tex](PX)^2:[/tex]

[tex](PX)^2 = 72/7 + 144 - 24PD + (PD)^2[/tex]

Simplifying, we find:

[tex](PX)^2 = 216/7 - 24PD + (PD)^2[/tex]

Since CP/PD = 1, we can write PD = 12 - PD, which gives us PD = 6.

Substituting this value into the equation, we have:

[tex](PX)^2 = 216/7 - 24(6) + (6)^2[/tex]

Simplifying further, we get:

[tex](PX)^2 = 72/7[/tex]

Taking the square root of both sides, we find:

PX = √(72/7) = 12√6/5

Similarly, we can prove that PY = 12√6/7.

For similar question on triangles.

https://brainly.com/question/17264112  

#SPJ11

The length of one leg of the triangle is equal to 7 units.

Based on Pythagorean theorem, the length of sides of a right-angled triangle are always in the ratio 1 : 1 : √2, which can be rewritten as follows;

x : x: x√2.

Where:

x represent the length of sides (one leg) of a right-angled triangle.

From this 45-45-90 triangle, we can determine the length of one leg of the triangle as follows:

x = 1/√2 × (7√2)

x = 7 units.

Read more on triangle here: https://brainly.com/question/3227590

#SPJ1

Complete Question:

The hypotenuse of a 45°-45°-90° triangle measures 7√2 units. what is the length of one leg of the triangle?

The value of measure of arc JK is,

⇒  (arc KJ) = 28 degree

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Measure of arc KL = 152°

Now, We know that;

⇒ m (arc LK) + m (arc KJ) = 180°

Substitute given values, we get;

⇒ 152° + m (arc KJ) = 180

⇒ m (arc KJ) = 180 - 152

⇒  (arc KJ) = 28 degree

Thus, The value of measure of arc JK is,

⇒  (arc KJ) = 28 degree

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

Answer:

yes agreed

Step-by-step explanation:

a+a=2a

b+b=2b

=2a+2b

The coordinates of the point X on the line segment is (-2/7, 48/7).

Given that, a point X on a segment with endpoints W(-2, 9) and Y(2, 4) partitions the segment in a 3:4 ratio.

Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:

P(x, y) = P(x, y) = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)]

Here, P(x, y) = [(3×2+4×(-2))/(3+4), (3×4+4×9)/(3+4)]

= (-2/7, 48/7)

Therefore, the coordinates of the point X on the line segment is (-2/7, 48/7).

To learn more about the coordinate geometry visit:

brainly.com/question/18269861.

#SPJ1

Answer: The cost of each sandwich (S) is $4 and the cost of each bottle of water (B) is $2.

Step-by-step explanation:

10S + 6B = 52 (Equation 1) -- Ramon's purchase

1S + 3B = 10 (Equation 2) -- Wallace's purchase

To solve these equations, we can use a method called substitution. We'll solve Equation 2 for S and substitute it into Equation 1:

From Equation 2, we can isolate S:

1S = 10 - 3B

S = 10 - 3B

Substituting S into Equation 1:

10(10 - 3B) + 6B = 52

100 - 30B + 6B = 52

100 - 24B = 52

-24B = 52 - 100

-24B = -48

B = -48 / -24

B = 2

Now, substitute the value of B back into Equation 2 to find S:

S + 3(2) = 10

S + 6 = 10

S = 10 - 6

S = 4

The number of more hotdog buns than kaya buns there are in the bakery, obtained from the fractions and ratios of the number of buns are 192 hotdog buns

A ratio is a quantitative representation of the number of times one quantity is contained in another quantity.

The fraction of the buns that are coffee buns = 3/11

The amount of the hotdog buns and kaya buns = The rest of the buns

The ratio of the hotdog buns to the kaya buns = 7 : 5

The total number of hotdog buns and kaya buns = 720 more than the number of coffee buns

The difference between the number of hotdog buns and kaya buns are therefore;

Let x represent the number of buns in the bakery

The number of coffee buns = 3·x/11

The number of hotdog buns and kaya buns = x - 3·x/11 = 8·x/11

8·x/11 = 3·x/11 + 720

Therefore;

8·x/11 - 3·x/11 = 720

5·x/11 = 720

5·x = 11 × 720 = 7920

x = 1584

The number of hotdog buns and kaya buns = 8×1584/11 = 1152

The number of hotdog buns = (7/(7 + 5)) × 1152 = 672

The number of kaya buns = (5/(7 + 5)) × 1152 = 480

The difference = 672 - 480 = 192

Part of the question, obtained from a similar question posted on the internet is; How many more hotdog buns than kaya buns are there in the bakery.

Learn more on ratios here: https://brainly.com/question/30828672

#SPJ1

11 x (7 + 5) = 132

(3/11) x 132 = 36 (coffee)

(8/11) x 132 = 96 (hotdog and kaya)

96 – 36 = 60

720/60 = 12

(2/12) x 96 = 16

16 x 12 = 192