Solve using double substitution

y=2x+5
6x-3y=6

Answer:

CQ=4 cm, BQ=8 cm

Step-by-step explanation:

In given triangle ABC draw the line MD parallel to the AQ.

1. Consider triangle AMD. In this triangle PQ║MD (build) and CP=PM (P is midpoint of CM). Then by the triangle midline theorem,  line PQ is midline of triangle AMD and CQ=QD.

2. Consider triangle BAQ. In this triangle AQ║MD and AM=MB. Then by the triangle midline theorem,  line MD is midline of triangle BAQ and BD=QD.

Hence, CQ=QD=BD. Since BC=12 cm and

BC=BQ+QD+BD,

then  

[tex]CQ=QD=BD=\dfrac{12}{3}=4\ cm.[/tex]

Note that

BQ=BD+QD=4+4=8 cm.

Final answer:

By examining the properties of median CM and midpoint P, we conclude that segment CQ is equal to QB, and both are 6 cm long in △ABC since CM bisects AB and BC is given as 12 cm.

Explanation:

The problem involves a triangle △ABC with CM being a median to side AB, and a line segment AP that intersects BC at point Q. According to the given information, P is the midpoint of CM, which implies that CP is equal to PM. Because BC is 12 cm in length, and CM is a median, we deduce that M is the midpoint of AB. This fact leads us to conclude that the triangles △CMB and △CMA are congruent by the Side-Side-Side (SSS) postulate, which means that CQ is equal to QB, and both are 6 cm long since Q lies on BC.

let's say that number is "x", so "x" is then the 100%.

we know 125 is the 500%, and "x" is the 100, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 125&500 \end{array}\implies \cfrac{x}{125}=\cfrac{100}{500}\implies \cfrac{x}{125}=\cfrac{1}{5} \\\\\\ 5x=125\implies x=\cfrac{125}{5}\implies x=25[/tex]

Answer:

30.85%

Step-by-step explanation:

Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10

mean = 70 and SD= 10

To find percentile we use z-score value

z value can be find using formula

[tex]z= \frac{x-mean}{SD}[/tex]

[tex]z= \frac{65-70}{10}[/tex]

z=-0.5

Now we use z- score table to find the value when z=-0.5

P(x=65) = 0.3085

To find percentile we multiply by 100

0.3085 * 100 = 30.85%

Answer:

mn=[tex]\sqrt{40}[/tex]

Step-by-step explanation:

m(2,5)n=(4,-1)

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

[tex]mn^{2}[/tex]=40

mn=[tex]\sqrt{40}[/tex]

Answer:

$32 is the sales price.

Step-by-step explanation:

First, change the percentage to a decimal.

60% = 60/100 = 0.6

Next, multiply 0.6 with the regular price ($80)

80 x 0.6 = 48

$48 is the discount. Subtract from the original price

80 - 48 = 32

$32 is the sales price.

~

Answer:

$32

Step-by-step explanation:

The sales price = original price - original price * discount rate

Factor out the original price

sales price = original price (1 -discount rate)

We know the original price is 80

We know the discount rate is 60% = .6

Substitute these values in

sales price = 80 (1-.6)

sales price = 80 * .4

sales price = 32

Answer:

x = 6

Step-by-step explanation:

We have to isolate x.

-282 = -6(5+7x)

Distribute.

-282 = -30 - 42x

Add 30 to both sides.

-252 = -42x

Divide both sides by -42.

6 = x

[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}=x^{\frac{3}{2}-\frac{1}{2}}=x^{\frac{3-1}{2}}=x^{\frac{2}{2}}=x^1=x\\\\Answer:\ \boxed{x}[/tex]

Answer:

Solution point (0,8)

Step-by-step explanation:

Multiply the top equation by 2

Now add the two equations together.

=================

Solve for x

==================

This one is just a bit messier. I made a graph of it just to show that the answer is correct.

Answer:

Therefore, Mid point : -2+5i.

Step-by-step explanation:

Given  :  Z1 = -8 + 3i and Z2 = 4 + 7i.

To find : What is the midpoint.

Solution : We have given  Z1 = -8 + 3i and Z2 = 4 + 7i.

Mid point :  [tex]\frac{z_{1}+z_{2}}{2}[/tex].

On plugging the values.

Mid point :  [tex]\frac{-8+3i + 4 +7i}{2}[/tex].

Combine like terms.

Mid point :  [tex]\frac{-8+4+3i +7i}{2}[/tex].

Mid point :  [tex]\frac{-4+10i}{2}[/tex].

Mid point : -2+5i.

Therefore, Mid point : -2+5i.

Answer:

7.6 in

Step-by-step explanation:

c = 2πr       Divide each side by 2π

r = C/2π     Insert values

r = 48/(2×3.14)

r = 48/6.28

r = 7.6 in

The probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.

To find the probability of getting exactly 4 tails when flipping a fair coin 6 times, we can use the binomial probability formula. The formula is:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

Plugging these values into the formula, we get:

P(X=4) = 15 * 0.5^4 * (1-0.5)^(6-4) = 15 * 0.0625 * 0.25 = 0.234375

So, the probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.

Answer:

equilateral triangle, kite, regular pentagon, regular hexagon

a hexagon has rotational symmetry. Furthermore, the angle of rotation is 60° and since there are six copies of 60° in 360° (360 ÷ 60 = 6), we have that the order of rotation of a regular hexagon is six.

let me know if none of these r choices on ur test i will give u more examples :)

Answer:c rolling pin

Step-by-step explanation:

1. c reflectional and point

2. a reflectional

3. d.reflectional, rotational and point

4. c. rolling pin

5. c 10

Substitute the values of w, x, y and z to the expression:

[tex]w=3,\ x=-2,\ y=6,\ z=0.5\\\\\dfrac{yz}{w}+2x=\dfrac{(6)(0.5)}{3}+(2)(-2)=\dfrac{3}{3}-4=1-4=-3[/tex]

Answer: -3

Step-by-step explanation:

Answer:

1  69/145 cups

Step-by-step explanation:

We can use ratio's to solve this problem.  We will put water over time

214 cups           x cups

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

145 hours        1 hours

Using cross products

214 *1 =145 x

Divide both sides by 125

214/145 = 145x/145

214/145 = x

145 goes into 215 1 time with 69 left over

1 69/145

The formula of a volume os a cylinder:

[tex]V=\pi r^2H[/tex]

r - radius

H - heihgt

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

If a cylinder and a cone have the same radius and height then the volume of a cone is three times smaller than a volume of a cylinder.

Therefore

[tex]V_{cone}=\dfrac{1}{3}V_{cylinder}[/tex]

We have

[tex]V_{cylinder}=72\ in^3[/tex]

Substitute:

[tex]V_{cone}=\dfrac{1}{3}\cdot72=24\ in^3[/tex]

Answer:

The equation of the line that passes through the points (-2, 3) and (2, 7) is   x - y + 5 = 0.

Step-by-step explanation:

Answer:

CL=9

Step-by-step explanation:

I'm sorry I can't explain it but the answer is 9.

The measure of CL is 9 m.

Given that, in ∆ABC, m∠C= 90° AL is an angle bisector m∠ABC = 30°, LB = 18 m.

We need to find the measure of CL.

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

Now, sin 30°=CL/BL

⇒ 1/2 = CL/18

⇒ CL=9 m

Therefore, the measure of CL is 9 m.

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Answer:

The correct option is D.

Step-by-step explanation:

In a linear function the rate of change is constant. It means either the function increase by a constant rate or function decrease by a constant rate.

In an exponential function the rate of change is not constant.

It is given that the population of bacteria increases by 30 every hour.

Since the population of bacteria increases by a constant rate therefore the population function is linear and it is defined as

[tex]P(t)=P_0+30t[/tex]

Where P₀ is initial population and t is time in hours.

Therefore correct option is D.

In the situation where a population of bacteria increases by a constant amount every hour, the growth pattern is linear, not exponential. Exponential growth in bacteria involves a doubling (or increase by a certain factor), not a fixed increase, and results in a J-shaped curve when plotted over time.

The situation presented in the question, where a population of bacteria increases by 30 every hour, represents a linear function. This is because the function increases by a constant amount. So, the answer is D. Linear, because the function increases by a constant amount. The given scenario differs from an example of exponential growth typically seen in bacteria. In exponential growth, the population of bacteria would double (or increase by a certain factor) each hour as opposed to increasing by a fixed amount. Exponential growth in bacteria occurs when there is an unlimited supply of nutrients, and the population size, when plotted over time, results in a J-shaped growth curve. Here, the rate of increase itself increases with time. In contrast, the linear growth described in the question indicates a steady rate of increase.

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Nala had lost 4,900 of her customers.

Hope this helps!

Answer:

Nala served 4,900 customers.

Step-by-step explanation:

5,000 to 100

5,000-100=4,900

YaY!!!  u got it!!!! =)

Answer:

d = [tex]\sqrt{26}[/tex] ≈ 5.1 ( to 1 dec. place )

Step-by-step explanation:

to calculate the distance d use the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = ([tex]\frac{5}{2}[/tex], 3) and (x₂, y₂ ) = ([tex]\frac{3}{2}[/tex], 8)

d =√ ([tex]\frac{3}{2}[/tex] - [tex]\frac{5}{2}[/tex])² - (8 - 3)²

  =[tex]\sqrt{1+25}[/tex] = [tex]\sqrt{26}[/tex] ≈ 5.1

The solution is $ 8.75

The sales tax amount Sandra will owe on the purchase is $ 8.75

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the price of the coat be = $ 49.99

Let the price of one skirt be = $ 24.99

The sales tax percentage of Sandra's purchase = 7 %

So , the price of 3 skirts = 3 x price of one skirt

Substituting the values in the equation , we get

The price of 3 skirts = 3 x 24.99

The price of 3 skirts = $ 74.97

Now , the total price of the purchase of Sandra = price of the coat + price of 3 skirts

Substituting the values in the equation , we get

The total price of the purchase of Sandra = $ 49.99 + $ 74.97

The total price of the purchase of Sandra = $ 124.96

And , the sales tax amount of the purchase by Sandra A = sales tax percentage of Sandra's purchase x total price of the purchase of Sandra

The sales tax amount of the purchase by Sandra A = ( 7/100 ) x 124.96

The sales tax amount of the purchase by Sandra A = 0.07 x 124.96

The sales tax amount of the purchase by Sandra A = $ 8.7472

Therefore , the value of A is $ 8.75

Hence , the sales tax amount of the purchase by Sandra is  $ 8.75

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Answer:

Step-by-step explanation:

1.20 x 5.75

=$6.90

The cost of petrol is given per gallon. Therefore, to find the cost of 5 3/4 gallons of petrol, multiply the cost per gallon which is 1.20 by the number of gallons, 5 3/4, that gives 6.90. Hence, 5 3/4 gallons of petrol would cost 6.90.

To find out the cost of 5 3/4 gallons of petrol, we first need to understand that the cost is listed per gallon. This means that for every gallon, you pay 1.20. So, to calculate the cost of 5 3/4 gallons, we just need to multiply the cost per gallon by the number of gallons.

So, the cost of 5 3/4 gallons would be: 1.20 (cost per gallon) x 5 3/4 (number of gallons) = 6.90.

Therefore, 5 3/4 gallons of petrol would cost 6.90.

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Answer:

draw out your diagram... if it was 1/2 draw one long shape (say it's a rectangle) and cut it once

Step-by-step explanation:

===/===

it should look something like this (represents 1/2)

All we have to do here is divide $13.50 by $0.90 to figure out how many guppies she can buy

$13.50 ÷ $0.90 = 15

Therefore, Karla can buy 15 guppies with $13.50

Hope this helps you

Brainliest would be appreciated

- AaronWiseIsBae

Answer: 52,642,000

47777,000+4865,000

You are correct. The answer is choice D

BD = BD by the reflexive property, which says that any segment is equal to itself

The hinge theorem says that the larger an angle is, the larger the opposite side will be. The converse goes in the opposite direction: if the side is larger, then the opposite angle is larger.

We know: The sum of measures of a tringle is equal 180°.

Therefore we have the equation:

m∠SQR + 58° + 35° = 180°

m∠SQR + 93° = 180°     subtract 93° from both sides

m∠SQR = 87°

Angles SQR and PQR are supplementary. The sum of the measures of supplementary angles is 180°.

Therefore:

x + 87 = 180     subtract 87 from both sides

Answer:

(g ∘ f)(-2) = 1

Step-by-step explanation:

f(x)=x^2

g(x)=x-3

(g o f)(-2)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(x^2)

(g o f)(x)=(x^2)-3

(g o f)(x)=x^2-3

x=-2→(g o f)(-2)=(-2)^2-3

(g o f)(-2)=(-2)(-2)-3

(g o f)(-2)=4-3

(g o f)(-2)=1