Is ΔFGH~ΔJKL? If so, identify the similarity postulate or theorem that applies.

Answer:

48 ft³

Step-by-step explanation:

The volume (V) of the pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)

Calculate h using the right triangle formed by a segment from the vertex to the midpoint of the base and across to the slant face ( the hypotenuse )

Using Pythagoras' identity on the right triangle then

h² + 3² = 5²

h² + 9 = 25 ( subtract 9 from both sides )

h² = 16 ( take the square root of both sides )

h = [tex]\sqrt{16}[/tex] = 4

area of square base = 6² = 36, hence

V = [tex]\frac{1}{3}[/tex] × 36 × 4 = 12 × 4 = 48 ft³

Answer:

1.75 miles

Step-by-step explanation:

If he rides around his block 3 times it is 1.5 miles and if he only rides around his block half-way not a time it is a quarter of a mile added on instead of a half.

Answer:

1 3/4

Step-by-step explanation:

3 1/2*1/2=1 3/4. Hope this helps.

Answer:

$7.15/hour

Step-by-step explanation:

Find Janie's unit rate of pay:  Amount per Hour:

$35.75 / (5 hours) = $7.15/hour

In each hour of working on Saturday morning, Janie earns $7.15.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Each Saturday morning Janie works five hours and earned $35.75.

So, To obtain the amount of money she earns each hour can be obtained by dividing the total amount she earned by the total number of hours she worked which is,

= $(35.75/5).

= $7.15.

So, Each hour Janie earns $7.15 by working in Saturday morning.

learn more about the unitary method here :

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Answer:

1 hour (60 minutes)

Step-by-step explanation:

If his speed remains the same, that means that this is a linear relationship.  y increases at the same rate as x increases.  Direct variation and all of that.  Because this is a linear relationship, it can be solved using proportions.  Set up the given info in a ratio with miles on the top and minutes on the bottom:

[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]

Now we want to know how long (unknown number of minutes) it will take him to go 12 miles.  Keep miles with miles and minutes with minutes:

[tex]\frac{miles}{minutes}:\frac{4}{20}[/tex]=[tex]\frac{12}{x}[/tex]

We can cross multiply now to get 4x = 12(20) and 4x = 240.  That means that x=60.  It will take him 60 minutes (1 hour) to go 12 miles.

Answer: 60 minuites

Step-by-step explanation: actully the dude thats on top of me its only 60 mins not 1hr and 60 mins

Step-by-step explanation:

[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ { \cos(theta) }^{2} = \frac{9}{16} \\ \: { \sin(theta) }^{2} = \frac{6}{16} = \frac{3}{8} \\ \: \sin(theta) = \frac{ \sqrt{3} }{ \sqrt{8} } \\ \sin(theta ) = \frac{ \sqrt{24} }{8}

= \frac{ 2\sqrt{6} }{8} = \frac{ \sqrt{6} }{4}

[/tex]

Answer:

[tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

sinx = [tex]\sqrt{1-cos^2x}[/tex]

sinΘ = [tex]\sqrt{1-(3/4)^2}[/tex]

        = [tex]\sqrt{1-\frac{9}{16} }[/tex] = [tex]\sqrt{\frac{7}{16} }[/tex] = [tex]\frac{\sqrt{7} }{4}[/tex]

Answer:

117

Step-by-step explanation:

182/14=13

13x9=117

Both x² and mx + b are differentiable functions of x (they are both polynomials), so if f(x) is also differentiable, we need to pay special attention at x = 2 where the two pieces of f meet.

Continuity means that the limit

[tex]\displaystyle \lim_{x\to2} f(x)[/tex]

must exist.

From the left side, we have x < 2 and f(x) = x², so

[tex]\displaystyle \lim_{x\to2^-} f(x) = \lim_{x\to2} x^2 = 4[/tex]

From the right, we have x > 2 and f(x) = mx + b, so

[tex]\displaystyle \lim_{x\to2^+} f(x) = \lim_{x\to2} (mx+b) = 4m+b[/tex]

It follows that 4m + b = 4.

Differentiability means that the limit

[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]

must exist.

From the left side, we again have x < 2 and f(x) = x². Then

[tex]\displaystyle \lim_{x\to2^-}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{x^2-4}{x-2} = \lim_{x\to2} (x+2) = 4[/tex]

From the right side side, we have x > 2 so f(x) = mx + b. Then

[tex]\displaystyle \lim_{x\to2^+}\frac{f(x)-f(2)}{x-2} = \lim_{x\to2} \frac{(mx+b)-(2m+b)}{x-2} = \lim_{x\to2} \frac{mx-2m}{x-2} = \lim_{x\to2}m = m[/tex]

The one-sided limits must be equal, so m = 4, and from the other constraint it follows that 16 + b = 4, or b = -12.

Answer:

$6

Step-by-step explanation:

$15.50 is $3.50 more than $12. And $12 is twice $6. The cost of the screwdriver is $6.

Check the picture below.

so the top and bottom segments are simply 7 units, we can read that off the grid.  Let's find the length of the other two segments, "c".

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ c=\sqrt{2^2+3^2}\implies c=\sqrt{13} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perimeter of the parallelogram}}{7+7+\sqrt{13}+\sqrt{13}}\qquad \approx \qquad 21.21[/tex]

Answer:

C: 30 units

Step-by-step explanation:

on edge 2021! hope this helps!!~ d=(´▽｀)=b

Answer:

  10 and 1

Step-by-step explanation:

Let x and y represent the two numbers. The problem statement lets us write two equations describing their relationships:

  x + y = 11

  x - y = 9

Adding these equations together, we have ...

  (x +y) +(x -y) = (11) +(9)

  2x = 20

  x = 10 . . . . . . . . . you will notice this is the average of the two given numbers

Then ...

  10 + y = 11 . . . . substitute for x in the first equation

  y = 1 . . . . . . . subtract 10

The two numbers are 10 and 1.

Answer:

  D)  x² + (y − 2)² = 52

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is the average of the end points:

  (h, k) = ((-6, 6) +(6, -2))/2 = (0, 4)/2 = (0, 2)

Then the distance between the center and an end point is the radius. It is found using the distance formula:

  r = √((x2 -x1)² +(y2 -y1)²) = √((-6 -0)² +(6 -2)²) = √(36 +16) = √52

Putting these values into the standard form equation for a circle ...

  (x -h)² +(y -k)² = r²

gives ...

  (x -0)² +(y -2)² = (√52)²

  x² +(y -2)² = 52 . . . . . matches choice D

[tex]

\sin(\beta)=\frac{y}{h} \\

\sin(27)=\frac{y}{350} \\

y=350\sin(27)\approx\boxed{158.9}

[/tex]

Step-by-step explanation:

0 = x² - 6x - 27

a = 1, b = -6, c = -27  Factor using AC method.

ac = (1)(-27) = -27

Factors of -27 that add up to -6 are -9 and 3.

Therefore:

0 = (x - 9) (x + 3)

x = -3, x = 9

The x-intercepts are (-3, 0) and (9, 0).

Answer:

375

Step-by-step explanation:

So first you would want to divide 1,500 by 4 because the ratio is 4:7. The answer you get if you divide 1,500 by 4 is 375. This is your answer because if you divide 1,500 by 4 you are seeing out of how many 'dentist' would recomend this product.

1500/4

375

Use a calculator

Very helpful

Answer:

The tall of the tree is about 109.85 feet

Step-by-step explanation:

* Lets study the situation in the problem

- The tree and its shadow formed a right angle triangle with legs

  x the tall of the tree and 125 feet the shadow of the tree

- Ellie and her shadow formed a right triangle with legs 4 feet and

 10 inches the tall of Ellie and 5.5 feet the shadow of Ellie

- The two triangles are similar

- There is an equal ratio between the corresponding sides of the

 similar triangles

# Ex: If triangles ABC and XYZ are similar

∴ AB/XY = BC/YZ = AC/XZ

* Lets use this rule to solve the problem

∵ The tall of the tree is x

∵ The tall of Ellie is 4 feet and 10 inches

- Lets change the tall of Ellie to feet only

∵ 1 foot = 12 inches

∴ 10 inches = 10/12 = 5/6 foot

∴ The tall of Ellie is 4 feet and 5/6 foot = 4 + 5/6 = 29/6 feet

∵ The shadow of the tree is 125 feet

∵ The shadow of Ellie is 5.5 feet

- By using similarity ratio

∴ Tall of tree/tall of Ellie = shadow of tree/shadow of Ellie

∴ x/(29/6) = 125/5.5 ⇒ using cross multiplication

∴ 5.5(x) = 125(29/6) ⇒ divide both sides by 5.5

∴ x ≅ 109.85 feet

* The tall of the tree is about 109.85 feet

Answer:

The tall tree is about 109.85

Step-by-step explanation:

Hope this helps!

Answer:

x = 29.91

Step-by-step explanation:

Cos (53) = 18/x

x = 18 / Cos(53)

x = 18/ 0.6018

x = 29.91

For this case we have that by definition of trigonometric relations of a rectangular triangle, that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle. Then, according to the figure we have:

[tex]cos (53) = \frac {18} {x}[/tex]

Clearing x:

[tex]x = \frac {18} {cos (53)}\\x = \frac {18} {0.60181502}\\x = 29,9095226969[/tex]

Rounding:

[tex]x = 29.91[/tex]

Answer:

29.91

[tex]\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}[/tex]

(X+5)^2+(y+6)^2=61 and then to find the radius take the square root of both sides

Answer:

288 ft.

Step-by-step explanation:

Find the perimeter. 50+50+94+94 = 288

Answer:

The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].

Step-by-step explanation:

Recall that   [tex]\sin(60\degree)[/tex]  is a special angle that can be obtained using an equilateral triangle.

The right triangle obtained using one of the lines symmetry was used to find the exact value of  [tex]\sin(60\degree)[/tex]  using SOH-CAH-TOA

The exact value of [tex]\sin(60\degree)[/tex] is [tex]\frac{\sqrt{3} }{2}[/tex].

Answer: OPTION A.

Step-by-step explanation:

We know that a circle measures 360 degrees. Then, to determine the size of a section, we need to multiply the percent of the category by 360 degrees.

First, we need to write 65 out of a hundred in decimal form:

[tex]\frac{65}{100}=0.65[/tex]

Now, let be "x" the degrees of the section representing 65 out of a hundred. We need to multiply 360 degrees by 0.65. Therefore, we get this result:

[tex]x=360\°*0.65\\x=234\°[/tex]

This matches with the option A.

The degree measurement for a section representing 65 out of 100 on a circle graph is 234 degrees. This is obtained by forming a ratio of the data point to the total data and multiplying by 360 (the total degrees in a circle).

To determine the degree measurement for a section on a circle graph, we must understand that a full circle consists of 360 degrees. The proportion that every bit of data takes in that circle is found by making a ratio of the data point to the total data multiplied by 360 degrees. Therefore, to find the proportion of 65 out of 100, we would make a ratio of 65 to 100 and multiply that by 360. Which comes out to: (65/100) * 360 = 234 degrees. So the correct answer would be 234 degrees (Option A).

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ANSWER

Step 2

EXPLANATION

The system of equations are:

Equation A:

[tex]y = 4 - 2z[/tex]

Equation B:

[tex]4y=2 - 4z[/tex]Step 1: Multiply equation A by -4.

Equation A:

[tex] - 4(y) = - 4(4 - 2z)[/tex]

Equation B:

[tex]4y=2 - 4z[/tex]

Step 2: Simplify equation A in step 1,

Equation A:

[tex] - 4y= - 16 + 8z[/tex]

This is where the student made the first error.

He didn't expand the second parenthesis correctly.

Answer:

The student made the first mistake in step 2.

Step-by-step explanation:

Answer:

slope = 5

Step-by-step explanation:

To calculate the slope m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 3) and (x₂, y₂ ) = (2, 8) ← ordered pairs from the table

m = [tex]\frac{8-3}{2-1}[/tex] = 5

The slope of a line can be calculated using the formula (y2-y1) / (x2-x1) using any two points on the line. The result you get from this calculation is the slope of the line.

To find the slope of a line from a set of coordinates, you need two points from the line. Let's consider these two points as (x1, y1) and (x2, y2). The formula for the slope is (y2-y1) / (x2-x1). This formula shows the change in y-values divided by the change in x-values, often referred to as 'rise over run'.

If, for instance, from your table the two points are (3,4) and (5,8), substitute these values into the formula: Slope = (8-4) / (5-3) = 4/2 = 2. So the slope of the line is 2.

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Answer:

A. 196 m²

Step-by-step explanation:

The two similar solids have volumes 1728 m³ and 343 m³.

The ratio of their side lengths is :

[tex]\sqrt[3]{1728}:\sqrt[3]{343}[/tex]

This simplifies to:

[tex]12:7[/tex]

If the surface area of the larger solid is  576 m², then the surface area of the smaller solid is given by:

[tex]\frac{7^2}{12^2}\times 576=196[/tex]

The correct answer is A

Answer:

The measure of angle LJC is [tex]m\angle LJC=43\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc LC

we know that

[tex]arc\ LC+arc\ JC=180\°[/tex] ----> because the diameter divide the circle into two equal parts

substitute the given values

[tex]arc\ LC+94\°=180\°[/tex]

[tex]arc\ LC=180\°-94\°=86\°[/tex]

step 2

we know that

The inscribed angle measures half that of the arc comprising

so  

[tex]m\angle LJC=\frac{1}{2}[arc\ LC][/tex]

substitute

[tex]m\angle LJC=\frac{1}{2}[86\°]=43\°[/tex]

Let X = the number.

You have 21 more than 3 times the number which is:

3x +21 = -15

Subtract 21 from both sides:

3x = -36

Divide both sides by 3:

x = -36 /3

x = -12

The answer is B.

Answer:

-13

Explanation:

Rewrite Equation:

(3 · x) + 21 = -15

Subtract 21 From Both Sides:

(3 · x) + 21 - 21 = -15 - 21

Simplify:

3x = -36

Divide Both Sides By 3:

[tex]\bold{\frac{3x}{3} \ = \ \frac{-36}{3} }[/tex]

Simplify:

x = -12

Mordancy.

Answer:

1.  0.75

2. -0.8

mark me brainlyest

First when looking at dialations, ignore the negative signs. They do not affect the expansion or contraction.

An expansion is any number greater than 1 and a contraction is any number less than 1.

Expansion: b) -2 and d) 2

Contraction: b) - 0.8 and d) 0.8

Answer:

A. 7.07 units

Step-by-step explanation:

Use the distance formula for coordinates:

[tex]d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2   }[/tex]

Fill in the coordinates accordingly:

[tex]d=\sqrt{(1-(-4))^2+(-3-2)^2}[/tex]

which simplifies down to

[tex]d=\sqrt{25+25}[/tex]

which is of course

[tex]d=\sqrt{50}[/tex]

Plug that into your calculator and you'll get the answer

Answer:

6 pairs of supplementary (when perpendicular)

a pair of complementary(0 for perpendicular)

4 pairs of adjacent

4 pairs of linear

2 pairs of vertical

Answer:

[tex]r=\frac{1}{3+2cos\theta}[/tex]

Step-by-step explanation:

Let us write the equations in standard form:

[tex]r=\frac{1}{3+2cos\theta} \implies r=\frac{\frac{1}{3} }{1+\frac{2}{3}\cos \theta }[/tex]

We have

[tex]e=\frac{2}{3}\:<\:1[/tex] and

 [tex]ep=\frac{1}{3}[/tex]

Since the eccentricity  of this conic is less than 1, the conic represents an ellipse.

The second equation is [tex]r=\frac{3}{2+3\sin \theta}[/tex].

This is a hyperbola, because eccentricity is more than 1.

The third equation is [tex]r=\frac{5}{2+2\sin \theta}[/tex].

This is a parabola, because eccentricity is  1.

The fourth equation is [tex]r=\frac{2}{2-3\sin \theta}[/tex].

This is also a hyperbola, because eccentricity is more than 1.