in the figure, ∆ABC ~ ∆DEF. solve for x

A) x = 1.5

B) x = 6

C) x = 4

D) x = 5.5​

Answer:

Option A is correct.

Step-by-step explanation:

The formula used for finding the volume of right cone is:

Volume of Right cone = (1/3)π.r².h

We need to find altitude i.e h

Volume of cone=V = 8579 m^3

Radius=r = 16m

Altitude =h =?

Putting values,

8579 = (1/3) * 3.14 * (16)^2*h

8579 = 1/3 * 3.14 * 256 *h

8579 = 267.95 * h

=> h = 8579/267.95

h = 32.0 m

So, Altitude of right cone is 32.0 m

Option A is correct.

Answer:

4.04 m

Step-by-step explanation:

El arbol y el suelo forman un angulo de 90°. Son los catetos de un triangulo rectangulo.

Los rayos solares forman un angulo de 60° con el suelo y forman la hipotenusa del triangulo.

Se tiene un triangulo rectangulo de angulos de 30°-60°-90°.

En este genero de triangulo, el cateto mayor mide [tex] \sqrt{3} [/tex] veces el cateto menor.

cateto menor = [tex] \dfrac{7}{\sqrt{3}} [/tex]

[tex] = \dfrac{7\sqrt{3}}{3} [/tex]

[tex] = 4.04 ~m [/tex]

The length of the shadow of the tree would be -

s = {7/√3}.

Given is that at a certain time of day the sun's rays make an angle of 60° with the ground.

Assume that the length of the shadow is [x] meters. Using the trigonometric ratios, we can write -

tan (60) = (height of tree {h})/(length of shadow {s})

sin(60)/cos(60) = (height of tree)/(length of shadow)

(√3/2)/(1/2) = {7/s}

√3/2 x 2 = 7/s

√3 = 7/s

s = {7/√3}

Therefore, the length of the shadow of the tree would be -

s = {7/√3}.

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{The question in english is -

At a certain time of day the sun's rays make an angle of 60° with the ground. What shade will the 7 m tall tree cast?}

Answer:

f=-5

Step-by-step explanation:

1) Add 12 to both sides

2) You should get f=-5

Answer:

[tex]\huge \boxed{F=-5}\checkmark[/tex]

Step-by-step explanation:

First, switch sides.

[tex]\displaystyle F-7=-12[/tex]

Then, add by 7 from both sides of equation.

[tex]\displaystyle F-7+7=-12+7[/tex]

Simplify, to find the answer.

[tex]\displaystyle -12+7=-5[/tex]

[tex]\huge \boxed{F=-5}[/tex], which is our answer.

Answer:

y=5/3  or y=1.67

Step-by-step explanation:

In this problem we have  that

(5x+8)=21x ----> given problem

21x-5x=8

16x=8

x=0.5

In the same way

Remember that the slope of a line is a constant

so

20y-2=17y+3

Solve for y

20y-17y=3+2

3y=5

y=5/3  or y=1.67

Answer:

The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi

Step-by-step explanation:

Given

18.60=2.60b+3

Here 18.60 is the total amount paid, 2.60 is the rate per mile and 3 is the charges for two passengers.

The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi i.e. b represents miles ..

the answer is: the solution b = 6 gives the number of miles the taxi traveled.

i just did the workbook :)

Answer:

5/9 from these categories can only be classified as rational and real.

Step-by-step explanation:

Natural numbers are counting numbers.  People don't ever say the number 5/9 when counting people. So 5/9 is not natural.

Whole numbers are counting numbers plus also including 0.  So we already said 5/9 is not natural and it is definitely not 0 so 5/9 is not whole.

Integers are whole numbers plus the opposite of the whole numbers.  5/9 is not whole and it is certainly not negative so we don't need to even consider if is the opposite of a whole number.

Rational numbers are numbers that can be expressed as a fraction where the top and bottom are integers. 5/9 is a rational number because 5 and 9 are whole numbers which are integers.

Irrational numbers are numbers that aren't rational. Our number 5/9 is rational so it isn't irrational.

Real numbers are any number that isn't imaginary. Doesn't include the imaginary unit. Our number doesn't include the imaginary unit so it is real.

Answer:

d. Rational Numbers

f. Real Numbers

Step-by-step explanation:

The number shown is 5/9

Let us see the options one by one

a. Natural numbers

Natural numbers consists of counting from 1 to infinity. The fractions are not included in the natural numbers hence it will not be the correct answer.

b. Whole numbers

Whole numbers is the set of natural numbers along with zero so it is also not the right answer.

c. Integers

Integers are combination of negative and positive whole numbers hence it is also not correct.

d. Rational numbers

Rational numbers are numbers which can be written in the form of p/q where p and belong to integers and q is not equal to zero. It is correct as the number is 5/9 where 5 is also an integer and 9 is also an integer. Also 9 ≠ 0 so 5/9 is a rational number.

e.  As the number is rational, it cannot be irrational

f. Real numbers

As real numbers is the set of all rational and irrational numbers, 5/9 will also be a part of the set .. Hence it is also correct ..

Answer:

x=-19/2  y=-33/2

Step-by-step explanation:

x − y = 7

y = 3x + 12

Substituting the second equation into the first

x − (3x+12) = 7

Distribute the minus sign

x-3x-12 = 7

Combine like terms

-2x-12 =7

Add 12 to each sid

-2x-12+12 =7+12

-2x=19

Divide each side by -2

-2x/-2 = 19/-2

x = -19/2

Now we need to find y

y = 3x+12

y = 3(-19/2) +12

y = -57/2 +24/2

y = -33/2

Answer:

(-19/2, -33/2)

Step-by-step explanation:

Answer:

y = -8

Step-by-step explanation:

It is given that,

-x - y = 7  ---(1)

x - y = 9  ---(2)

To find the solution

Add eq (1) and eq(2) we get

-x - y = 7  ---(1)

x - y = 9  ---(2)

0 - 2y  = 16

y = 16/(-2) =  -8

Substitute the value of y in eq(1)

-x - y = 7  ---(1)

-x - -8 = 7

-x + 8 = 7

x = 8 - 7 = 1

Therefore x = 1 and y = -8

Answer:

Option B [tex]28.53\ units^{2}[/tex]

Step-by-step explanation:

The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADC

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  

a,b,c be the lengths of the sides of a triangle.  

The area is given by:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]

where

p is half the perimeter

[tex]p=\frac{a+b+c}{2}[/tex]

step 1

Find the area of triangle ABD

we have

[tex]a=AB=2.89\ units[/tex]

[tex]b=BD=8.59\ units[/tex]

[tex]c=DA=8.6\ units[/tex]

Find the half perimeter p

[tex]p=\frac{2.89+8.59+8.6}{2}=10.04\ units[/tex]

Find the area

[tex]A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]

[tex]A=\sqrt{10.04(7.15)(1.45)(1.44)}[/tex]

[tex]A=\sqrt{149.89}[/tex]

[tex]A=12.24\ units^{2}[/tex]

step 2

Find the area of triangle ADC

we have

[tex]a=AC=4.3\ units[/tex]

[tex]b=AD=8.6\ units[/tex]

[tex]c=DC=7.58\ units[/tex]

Find the half perimeter p

[tex]p=\frac{4.3+8.6+7.58}{2}=10.24\ units[/tex]

Find the area

[tex]A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]

[tex]A=\sqrt{10.24(5.94)(1.64)(2.66)}[/tex]

[tex]A=\sqrt{265.35}[/tex]

[tex]A=16.29\ units^{2}[/tex]

step 3

Find the total area

[tex]A=12.24+16.29=28.53\ units^{2}[/tex]

Answer:

B.) 28.53 units²

Step-by-step explanation:

I got it correct on founders edtell

Answer:

B. Unimodal-Skewed

Step-by-step explanation:

A distribution is called unimodal if it has only one hump in the histogram.

A symmetric distribution is equally divided on both sides of the highest hump.

The given histogram has only one hump at 4 and as it is not symmetrically distributed, it is skewed.

So the correct answer is:

B. Unimodal-Skewed ..

Answer:

B. Unimodal Skewed

Step-by-step explanation:

The Histogram given in figure has one peak and it is skewed to the right So, it is Right Skewed Unimodal Histogram.

Moreover, Unimodal means the distribution has one peak, Skewed means this peak is present in either the left or right side of the center of the distribution.

Option A is incorrect because the given histogram is not symmetric, it is skewed distribution.

Option C can't be taken because uniform means the size of bars is approximately same for the given distribution.

Options D & E is not correct because the given distribution is not Bimodal it has only one peak.

Answer:

4x^2/4x^2-x-3

Step-by-step explanation:

boomchakalaka

The quotient is 4x²/4x²-x-3.

In mathematics, a quotient is a quantity produced with the aid of the department of numbers.

The quotient is the solution acquired whilst we divide one range by using every other. for example, if we divide the quantity 4 by means of 2, we get the end result as 2, that's the quotient.

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Answer:

Order of symmetry = 1

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

The given shape, when rotated will only have the shape like original shape after one complete rotation so the order of symmetry is one ..

Answer:

1934.2

Step-by-step explanation:

3.14*14=43.98 squared=1934.2

Answer:

615.75

Step-by-step explanation:

Use A = πr², letting r = 14, so that:  

A = π(14)²  

≈ 615.75 ft²

Rounding to the nearest hundredth would make the answer 618

Answer:

[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]

Explanation

The directrix y=7, is above the y-value of the focus. The parabola must will open downwards.

Such parabola has equation of the form,

[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]

where (h,k) is the vertex.

The vertex is the midway from the focus to the directrix

The x-value of the vertex is x=-5 because it is on a vertical line that goes through (-5,-5).

The y-value of the vertex is

[tex]y = \frac{ 7 + - 5}{2} [/tex]

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

The equation of the parabola now becomes

[tex]{(x + 5)}^{2} = - 4p(y - 1)[/tex]

p is the distance from the focus to the vertex which is p=|7-1|=6

Substitute the value of p to get:

[tex]{(x + 5)}^{2} = - 4 \times 6(y - 1)[/tex]

[tex]{(x + 5)}^{2} = - 24(y - 1)[/tex]

We solve for y to get:

[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]

Answer:

f(x) = −one twentyfourth (x + 5)2 + 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{8(5)+2(4)+5(3)+6(2)+5(1)}{26}[/tex]

Now we simplify:

[tex]\frac{80}{26}[/tex]

[tex]\frac{40}{13}[/tex]

Now we divide:

[tex]3.1[/tex]

Answer:

15x < 200; x < 13.33; the maximum price for a pair of shorts

Step-by-step explanation:

1. Set up the inequality

Let x = price of a pair of shorts. Then

 15x = price of shorts for the team

You have one condition:

15x < 200

2. Solve the inequality

[tex]\begin{array}{rcl}15x & < & 200\\\\x & < & \dfrac{200}{15}\\\\x & < & \mathbf{13.333}\\\end{array}[/tex]

3. Meaning of solution

The solution represents the maximum price the coach can pay for a pair of shorts.

If the coach pays $13.33 per pair, the total cost for the team will be $199.95, and the condition is satisfied.

Answer: The coach may spend up to $13.33 per pair of shorts.

Step-by-step explanation:

Hi, to answer this question we have to write an inequality with the information given:

So, we have to multiply the number of shorts by the price of each one, we will represent the price with the variable "x".(15x)

That cost must be equal or less to 200.

Mathematically speaking

15 x ≤ 200

Solving for x

x ≤200/15

x ≤ 13.33

This solution represents that the coach may spend up to $13.33 per pair of shorts.

Feel free to ask for more if needed or if you did not understand something.

Answer:

D. 35 degrees.

Step-by-step explanation:

125 = p + 90 (by the external Angle of a Triangle theorem).

p = 125 - 90

p = 35 degrees (answer).

Answer:

35 degrees

Step-by-step explanation:

Ok so that angle that has the 125 degree is adjacent to an angle inside the triangle. These adjacent angles are actually supplementary because they are formed by a straight-edge. So the angle inside adjacent to the 125 degree angle is 180-125=55 degrees.

Same logic applies to angle adjacent to the 90 degree angle. The angle adjacent to the 90 degree angle is also supplementary to the 90 degree angle. So 180-90=90 degrees for the other inside angle next to the 90 degree angle.

So the figure formed here is a triangle.  The angles in this triangle should add up to be 180 degrees.  So we have the equation 90+55+p=180.

Let's solve this by first simplifying the 90+55 part!

145+p=180

Subtract 145 on both sides:

p=180-145

Simplify.

p= 35 degrees

Answer:

3.5 hours

Step-by-step explanation:

5 x 70 = 350

7 x 65 = 455

350 + 455 = 805

1050 - 805 = 245

245/ 70 = 3.5

They will take an additional 3.5 hours on the third day to reach their destination.

Explanation of the distance covered in the first two days and how much more time it will take on the third day to reach their destination.

The distance covered in the first two days can be calculated using the formula:

Distance = Speed x Time

Therefore, after the first two days, they have covered a total distance of 350 + 455 = 805 miles. They have 1050 - 805 = 245 miles left to travel.

On the third day, at an average speed of 70 mph, they will cover the remaining 245 miles. Therefore, the time it will take for them to reach their friends' home on the third day is:

Time = Distance / Speed = 245 miles / 70 mph = 3.5 hours

They will take an additional 3.5 hours on the third day to reach their destination.

EF = 12

KF = 6

LF = 7.8

LK = sqrt(7.8^2-6^2) = 4.98

IJ = LK

Answer with explanation:

→ΔELF ≅ Δ GHJ-------[Given]

→EF=GH----------[CPCT]

→GJ=FL-------[CPCT]

Let , O be the center of the circle.

→ EK=KF--------[Perpendicular from the center to the chord bisects the chord.]

→GI=IH------[Reason same as Above]

→→EK=GI, KF=HI

→→OJ=OL

→OK=KI

→OJ-OK=OL-KI

→LK=IJ

⇒→Δ LKF ≅ Δ JIG-------[SAS]

Now, In Δ LKF, By Pythagorean Theorem

 →(LF)²=(LK)²+(KF)²

→(7.8)²=(LK)²+(6)²

→60.84-36=(LK)²

→24.84=(LK)²

LK=4.98

→→LK=IJ=4.98

Option C:→4.98

Answer:

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

Step-by-step explanation:

Given

9 - 3x = 7 ( subtract 9 from both sides )

- 3x = - 2 (divide both sides by - 3 )

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

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

Add [tex]3x[/tex] on both sides. [tex]9=7+3x[/tex]

Subtract 7 from both sides. [tex]2=3x[/tex]

Divide both sides by 3. [tex]\boxed{\frac{2}{3}}=x[/tex]

Answer:

Option C step 3

Step-by-step explanation:

we have

-14x-2y=24 ------> equation A

14x+8y=-12 -----> equation B

step 1

Solve the system by elimination

Adds equation A and equation B

-14x-2y=24

14x+8y=-12

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

-2y+8y=24-12

6y=12

The step 1 is correct

step 2

Solve for y

Divide by 6 both sides

6y/6=12/6

y=2

The step 2 is correct

step 3

Find the value of x

substitute the value of y in the equation A

-14x-2(2)=24

-14x-4=24

14x=-4-24

14x=-28

x=-2

The step 3 is not correct

therefore

Petro first make a mistake in Step 3

Answer:

Step 3 in the correct answer. Thx. Just to verify with everyone it is step 3.

Step-by-step explanation:

On Edge 2020 got it correct.

Answer:

she can make 50 different selections!

Step-by-step explanation:

To find the different selections that can be made, we use the formula:

nCr = n! / r! * (n - r)!. Where 'n' represents the number of items available and 'r' represents the nuber of items being chosen

In this case:

'n' equals 10 and 'r' equals 2. Therefore:

[tex]10C_{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{90}{2} =50[/tex]

So she can make 50 different selections!

Answer: 45

Step-by-step explanation:

The combination of n things taking r at a time is given by :-

[tex]C(n;r)=\dfrac{n!}{(n-r)!}[/tex]

Given : Lucy Furr must supply 2 different bags of chips for a party.

She finds 10 varieties at her local grocer.

Then the number of different selections she can make is given by :-

[tex]C(10;2)=\dfrac{10!}{2!(10-2)!}\\\\=\dfrac{10\times9\times8!}{2\times8!}=\dfrac{90}{2}=45[/tex]

Hence, the number of different selections she can make= 45

Answer:

[tex]\large\boxed{(x+y)^2:(x-y)^2=49}[/tex]

Step-by-step explanation:

[tex]3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------[/tex]

[tex](x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49[/tex]

Answer:

102 steps/1minute

In seconds it would be 102/60 which can be reduced to 17/10, or 1.7

Answer:

C. -2x-4

Step-by-step explanation:

-3 - 3x – 1 + x

Combine like terms

-3 -1     -3x +x

-4 -2x

Rearrange the order to put the x term first

-2x-4

c

just got it right on edge

Answer:

OPTION C

Step-by-step explanation:

We know that the toll road is 4 times faster than the side streets.

If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{4} x[/tex] represents the time she takes taking the toll road.

Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:

[tex]y = \frac{1}{4}x + 30[/tex]

Therefore, the correct solution is the OPTION C.

Answer:

c

Step-by-step explanation:

took the test but give the other guy brainliest he deserves it

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x+\dfrac{15}{2}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==================================[/tex]

[tex]\text{We have}\ y=-4x-1\to m_1=-4\\\\\text{Therefore}\ m_2=-\dfrac{1}{-4}=\dfrac{1}{4}.\\\\\text{The equation of a line perpendicular to}\ y=-4x-1:\\\\y=\dfrac{1}{4}x+b\\\\\text{Put the coordinates of the point (-2, 7) to the equation:}\\\\7=\dfrac{1}{4}(-2)+b\\\\7=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\7\dfrac{1}{2}=b\to b=7\dfrac{1}{2}=\dfrac{7\cdot2+1}{2}=\dfrac{15}{2}\\\\\text{Finally:}\\\\y=\dfrac{1}{4}x+\dfrac{15}{2}[/tex]

Answer:

3 5/6

Step-by-step explanation:

3 1/2 plus 2 2/3 equals 6 1/6. 10 minus 6 1/6 equals 3 5/6. So they still need to lose 3 5/6 pounds to reach their go of losing 10 pounds.

let's firstly convert the mixed fractions to improper fractions, and then subtract.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{goal}}{10}-\stackrel{\textit{first week}}{\cfrac{7}{2}}-\stackrel{\textit{second week}}{\cfrac{8}{3}}\implies \cfrac{10}{1}-\cfrac{7}{2}-\cfrac{8}{3}\implies \stackrel{\textit{using an LCD of 6}}{\cfrac{(6)10-(3)7-(2)8}{6}} \\\\\\ \cfrac{60-21-16}{6}\implies \cfrac{23}{6}\implies 3\frac{5}{6}[/tex]

Answer:

C

Step-by-step explanation:

O x² + 9x -3x – 27 = (x + 9)(x – 3)

x² + 6x - 27 = (x + 9)(x - 3)