Write an equation of the line that is parallel to y = 1 2 x + 3 and passes through the point (10, -5).

Answer:

The correct choice is C

Step-by-step explanation:

The given curve is described by the parametric equations:

[tex]x=4-t[/tex]

[tex]y=t^2-2[/tex]

Let us eliminate the parameter by making t the subject in the first equation and substitute into the second equation;

[tex]t=4-x[/tex]

We substitute this into the second equation to get:

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

This is the equation of a parabola whose vertex is at (4,-2)

The correct choice is C

Answer:

x =16

Step-by-step explanation:

You can use Theorem Pythagoras method to solve this question.

The formula is a^2 + b^2 =c^2

In this question a=x , b=12, and c= 20

to find a which means x you should use this formula : c^2 - b^2=20^2-12^2

= 400 - 144

=√256

=16

You also can use another method by using the second diagram.

In that diagram you have to know that 12÷3 is 4, 20÷5 is 4, hence x÷4 is 4

so , x=16.

I hope this two ways for answering this question will be helpful for you.

Answer:

x = 16

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] ( cross- multiply )

5x = 4 × 20 = 80 ( divide both sides by 5 )

x = 16

The probability that an item is either Large or Blue, [tex]\( P(\text{Large or Blue}) \)[/tex], is 0.7 after simplification.

To find the probability [tex]\( P(\text{Large or Blue}) \)[/tex], we will use the principle of inclusion-exclusion. The formula for two events A and B is:

[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]

Let's define our events as:

- A = The event that an item is Large.

- B = The event that an item is Blue.

Looking at the table:

- The probability that an item is Large, [tex]\( P(\text{Large}) \)[/tex], is the sum of all Large items divided by the total number of items.

- The probability that an item is Blue, [tex]\( P(\text{Blue}) \)[/tex], is the sum of all Blue items divided by the total number of items.

- The probability that an item is both Large and Blue, [tex]\( P(\text{Large and Blue}) \)[/tex], is the number of items that are both Large and Blue divided by the total number of items.

From the table:

Now we can calculate the probabilities:

[tex]\[ P(\text{Large}) = \frac{25}{40} \][/tex]

[tex]\[ P(\text{Blue}) = \frac{20}{40} \][/tex]

[tex]\[ P(\text{Large and Blue}) = \frac{17}{40} \][/tex]

Using the inclusion-exclusion principle:

[tex]\[ P(\text{Large or Blue}) = P(\text{Large}) + P(\text{Blue}) - P(\text{Large and Blue}) \][/tex]

Let's do the calculations.

The probability of an item being Large or Blue is [tex]\( P(\text{Large or Blue}) = 0.7 \)[/tex], which is already in its simplest form.

Answer:

  a) 708.00

  b) 108.00

  c) 11

Step-by-step explanation:

a) The cost is $59 for each of 12 months, so the total cost is ...

  12×$59 = $708

__

b) The "carrying charges" are the difference between what is paid and the cash price:

 $708 -600 = $108

__

c) Saving at the rate of $59 per month, it will take ...

  $600/($59/mo) ≈ 10.17 mo

to save the money. The amount saved will be $590, or $10 short of the required amount after 10 months, so it will take 11 months to save enough for the cash purchase.

Answer:

 a) 708.00

 b) 108.00

 c) 11

Step-by-step explanation:

Congruent means they are the same. Match the letter with the corresponding dimension on the other cone.

A = 6.2/2 = 3.1 units

B = 4.2 units

C = 5.2 units

D = 42 units^3

The unknown measures of the cones are A = 3.1, B = 4.2, C = 5.22 and D = 42 units³

Two figures are said to be congruent if they have the same shape and the their corresponding sides are the same.

Given that both cones are congruent. Hence:

A = 6.2 / 2 = 3.1

B = 4.2

Using Pythagoras:

C² = A² + B²

C² = 3.1² + 4.2²

C = 5.22

D = 42 units³

The unknown measures of the cones are A = 3.1, B = 4.2, C = 5.22 and D = 42 units³

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Answer:

3a5b

Step-by-step explanation:

Answer:

3a5b

Step-by-step explanation:

Answer:

[tex]3a^4[/tex]

Step-by-step explanation:

Given expression is [tex]27a^{12}[/tex].

Now we need to find the cube root of given expression [tex]27a^{12}[/tex].

[tex]\sqrt[3]{27a^{12}}[/tex]

[tex]=\sqrt[3]{3*3*3a^{4*3}}[/tex]

[tex]=\sqrt[3]{3^3\left(a^4\right)^3}[/tex]

[tex]=\sqrt[3]{\left(3a^4\right)^3}[/tex]

Since cube root and cube are opposite operations of each other. So they will cancel each other.

[tex]=3a^4[/tex]

Hence correct choice is the last choice [tex]3a^4[/tex].

Answer:

(10 yd) ............=x.....

ANSWER

9.6

EXPLANATION

The given trigonometric equation is:

[tex] \cos(21 \degree) = \frac{9}{y} [/tex]

We want to find y, so we multiply both sides by y to get,

[tex]y\cos(21 \degree) = \frac{9}{y} \times y[/tex]

Cancel out the common factors,

.

[tex]y\cos(21 \degree) = 9[/tex]

. Divide both sides by cos(21°)

[tex]y= \frac{9}{\cos(21 \degree)} [/tex]

[tex]y = 9.64[/tex]

To the nearest tenth, y=9.6

Answer:

64/3 cc or 64/3 cm³

Step-by-step explanation:

The formula for the volume of a triangular pyramid is

V = (1/3)(area of base)(height)

Here we have a square prism (actually, a cube), whose square base is 4 cm by 4 cm (4 cm is the cube root of 64 cc).  The height of this cube is also 4 cm.

The volume of a triangular pyramid of base area (4 cm)² and height 4 cm is

V = (1/3)(base area)(height)

   = (1/3)(16 cm²)(4 cm) = 64/3 cc

Answer:

64/3 cc or 64/3 cm³

Step-by-step explanation:

Answer:

(D)[tex]x=104^{\circ}[/tex]

Step-by-step explanation:

Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

To find: the value of x.

Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore

[tex]{\angle}ABC+{\angle}ADC=180^{\circ}[/tex]

Substituting the given values, we have

[tex]91^{\circ}+x-15^{\circ}=180^{\circ}[/tex]

[tex]x+76^{\circ}=180^{\circ}[/tex]

[tex]x=104^{\circ}[/tex]

thus, the value of x is [tex]104^{\circ}[/tex].

Hence, option D is correct.

Answer:

the answer is 104 i just took quiz 6.11.3

Step-by-step explanation:

Answer:

The measure of angle JKL is m∠JKL=35°

Step-by-step explanation:

step 1

Find the measure of the arc KL

we know that

arc KL+arc KN+arc NL=360° ----> by complete circle

arc KL+150°+140°=360°

arc KL=360°-290°=70°

step 2

Find the measure of angle JKL

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠JKL=(1/2)[arc KL]

substitute

m∠JKL=(1/2)[70°]=35°

Answer: (3b + 5)(3b - 5)

Because both terms, 9b² and 25, are perfect squares, you can factor by taking the square roots of both terms.

The square root of 9b² is 3b (3b × 3b = 9b²).

The square root of 25 is 5 (5 × 5 = 25).

9b² - 25 has a negative, so the factored expression would be

(3b + 5)(3b - 5). The signs (+ and -) alternate in this case because the  expression, 9b² - 25, has no middle term.

You can check your work by using FOIL. See the attachment below.

F irst

O utside

I nside

L ast

Answer:

(3b + 5)(3b - 5)

Step-by-step explanation:

(3b + 5)(3b - 5)

A prism is rectangular shaped,. a pyramid is triangular shaped.

The ratio would be  1 to 3

The formula for the pyramid is V = 1/3Bh

Answer:

The size of Harry's loan is $9000.

Step-by-step explanation:

D(t) models Harry's remaining debt, in dollars, as a function of time t, in months  that is given by :

[tex]D(t) =-200t+ 9000[/tex]

We can see 200 is in negative that means it is getting deducted from the function. So, Harry must be paying this each month against his loan.

Lets put t = 0, that shows no payments have been made.

This will get the amount of loan, before any payments.

[tex]D(t)=-200(0)+9000[/tex]

So,[tex]D(t) =9000[/tex]

Hence, the size of Harry's loan is $9000.

Answer:

$200

Step-by-step explanation:

I got $9000 wrong on Khan and $200 right

Answer:

25 ft

Step-by-step explanation:

The tree's shadow is 4 times the length of the man's shadow, so we presume the tree is 4 times the height of the man: 4 × (6 ft 3 in) = (24 ft 12 in) = 25 ft.

Answer:  B) 1.6

Step-by-step explanation:

[tex]P=100e^{0.70t}\\\\\underline{\text{Substitute P = 300:}}\\300=100e^{0.70t}\\\\\\\underline{\text{Divide both sides by 100:}}\\3=e^{0.70t}\\\\\\\underline{\text{Apply ln to both sides:}}\\ln\ 3=ln\ e^{0.70t}\\\\\\\underline{\text{ln e cancels out:}}\\ln\ 3=0.70t\\\\\\\underline{\text{Divide both sides by 0.70:}}\\\dfrac{ln\ 3}{0.70}=t\\\\\\\underline{\text{Evaluate using a calculator:}}\\1.569=t[/tex]

See attachment for solution steps and answer.

The slope of the line through the points (-1,6) and (7,-2) is -1. Substitute this and one of the points into the point-slope form, 'y - y1 = m (x - x1)', to get the equation of the line. The final equation is y = -x + 5.

To complete the equation of the line through points (-1,6) and (7,-2), we first need to find the slope (m) of the line using the formula m=(y2-y1)/(x2-x1). Here, (-1,6) is (x1,y1) and (7,-2) is (x2,y2). When we substitute these values in, we get m=(-2-6)/(7-(-1)), which simplifies to m=-8/8 or m=-1.

Now, you can use the point-slope form of a line, which is y - y1 = m (x - x1). You can use either of the points given, but let's use (-1,6). The equation then becomes y - 6 = -1(x - (-1)). To simplify, this becomes y - 6 = -x - 1. If you add 6 to both sides, the final equation of the line is y = -x + 5.

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Final answer:

The slope of a line perpendicular to a line with slope 3/4 is -4/3. This follows from the principle that slopes of perpendicular lines are negative reciprocals of each other.

Explanation:

The question pertains to finding the slope of a line that is perpendicular to another line with a given slope. Given that the slope (m) of line l is 3/4, let's find the slope of line m which is perpendicular to l. In algebra, the slope of perpendicular lines are negative reciprocals of each other. This means that to find the slope of m, you take the negative reciprocal of 3/4, which is -4/3.

Thus, the correct answer is C. - 4 over 3.

Answer:

y = ln( x + 6 ) - 11

h = 6

k = -11

h + k = -5

Step-by-step explanation:

Horizontal shift changes whats inside the brackets, in other words, changes just the x-value.If the shift is right, the number should be subtracted, if the shift is left, the number should be added.

Vertical shift changes the equation as a whole.if the shift is up, the number of should be added.If the shift is down, the number should be subtracted.

The changes given to us are 3 units left ( horizontal translation ) and 5 units down ( vertical translation )

If we rewrite the equation, we have:

y = ln( x + 3 + 3 ) - 6 - 5

y = ln( x + 6 ) - 11

Answer:

It is B because this triangle Q and R are congruent

Step-by-step explanation:

Answer:

B. 68

Step-by-step explanation:

Because the side lengths PQ and PR both equal 5 and are congruent, the angles opposite them (angle Q and angle R) are also congruent to each other.

Angle Q is 68, so angle R is also 68.

The expression 6(x − 5) means the product of 6 and the difference of x minus 5. If x = 7, the value of the expression is 12.

We can see that the number 6 to the left of the expression 6(x - 5), this means 6 times (x - 5), The reason we write it that way is because the multiplication symbol, ×, can be confused with the variable x, follow by (x - 5) which is the difference of x minus 5. All together is the product of 6 and the difference of x minus 5.

If x = 7, then:

6(7 - 5) = 6(2) = 12

Following are the solution to the given expression:

Given:

[tex]6(x-5) \\\\ x=7 [/tex]

To find:

value=?

Solution:

[tex]\to 6(x-5)\\\\ [/tex]

putting the x value into the above expression:

[tex]\to 6(7-5)\\\\ \to 6(2)\\\\ \to 12[/tex]

Therefore the final answer is "12".

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Answer:

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is -80 feet per second.

Step-by-step explanation:

The function that models the height of the ball is:

[tex]f(t)=-16t^2+48t=160[/tex]

At t=3, [tex]f(3)=-16(3)^2+48(3)+160=160[/tex]

At t=5, [tex]f(5)=-16(5)^2+48(5)+160=0[/tex]

The average rate of change is simply the slope of the secant line connecting.

[tex](3,f(3))[/tex] and [tex](5,f(5))[/tex].

The average rate of change

[tex]=\frac{f(3)-f(5)}{3-5}[/tex]

[tex]=\frac{160-0}{-2}[/tex]

[tex]=-80fts^{-1}[/tex]

Answer: B) 0.40 mi

Step-by-step explanation:

Using the Pythagorean Theorem.

A squared + B squared = C squared.

A = leg B = leg C = hypotenuse

A = 0.3 B = ? C = 0.7

0.3 squared x ? squared = 0.7 squared

Answer:

on usatestprep its 0.63

Step-by-step explanation:

Answer:

430/5*9 = 774 miles

Step-by-step explanation:

I am pretty sure it’s step one

Answer:

what

Step-by-step explanation:

Answer:

B. greater mean = class B greater median = class B

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

You need to use the Pythagorean theorem. Which is a^2+b^2=c^2

so 5^2+12^2

which simplifies to 25+144=c^2

then it simplifies to 169=c^2

Now you take the square root

c=sqrt(169)

c=13

For this case we have that by definition, the Pythagorean theorem states that:

[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]

Where:

c: It is the hypotenuse

a, b: Are the legs

Substituting the values of the figure:

[tex]c = \sqrt {5 ^ 2 + 12 ^ 2}\\c = \sqrt {25 + 144}\\c = \sqrt {169}\\c = 13[/tex]

Thus, the value of the hypotenuse is 13.

Answer:

13

Option B

Answer:

The fraction will decrease [tex]33.33\%[/tex]

Step-by-step explanation:

Let

x/y ----> the fraction

we know that

100%-50^=50%=50/100=0.50

100%-25%=75%=75/100=0.75

substitute

[tex]\frac{x}{y}*\frac{0.50}{0.75} =\frac{2}{3}(\frac{x}{y})[/tex]

therefore

The percent that the fraction will decrease is equal to

[tex](1-\frac{2}{3})*100=33.33\%[/tex]

It will take them 30 minutes

The faster computer will take approximately 22.5 minutes to do the job on its own.

Let's assume that the faster computer can complete the job on its own in x minutes.

If the slower computer takes 45 minutes to complete the job on its own, it means that in 1 minute it completes 1/45th of the job.

Working together, the two computers can complete the entire job in 15 minutes. So in 1 minute, they can complete 1/15th of the job.

Therefore, 1/45 + 1/x = 1/15

Simplifying the equation, we get 1/x = 1/15 - 1/45

Substituting the numerator values with a common denominator, 1/x = (3/45) - (1/45) = 2/45

Now, solving for x, we get x = 45/2 = 22.5

So, it will take the faster computer approximately 22.5 minutes to do the job on its own.

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