Answer:
x=29
Step-by-step explanation:
3x-13=74
We want to solve for x, so we need to isolate it.
The first step is to add 13 to each side.
3x-13+13=74+13
3x = 87
Then we divide by 3 on each side
3x/3 = 87/3
x= 29
In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈ CM and a line AP intersecting BC at point Q. Find the lengths of segments CQ and BQ , if P is the midpoint of CM
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.
evaluate the expression when w=3,x=-2,y=6 and z=0.5
yz/w + 2x
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:
2700=300•2^10x solve for x
125 is 500% of what number
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]
Given: ∆ABC, m∠C = 90° AL - is an angle bisector m∠ABC = 30°, LB = 18m Find: CL
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.
What is an angle bisector?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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Help please ?
What is the missing statement in the two column proof ?
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.
Nala has 5,000 customers now she has 100 how many customers did she went away
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!!!! =)
is the length of MN on graph
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]
If Petrol cost 1.20 per gallon how much would 5 3/4 cost?
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.
Explanation: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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Karla can buy guppies for $0.90 each at the corner pet store. If she has $13.50, how many guppies can she buy?
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
what is the value of X
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
x = 93What is the equation of the line-2,3 and 2,7
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:
F Gucci sells 47777,000 a month and if Chanel sells 4865,000 how much is together
Answer: 52,642,000
47777,000+4865,000
Sandra bought a new coat for $49.99 and 3 skirts for $24.99 each . If the Sale tax rate is 7% to the nearest cent what is the amount of sale tax Sandra will owe on the purchase?
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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The spoke of wheel reaches from the center of the wheel to its rim if the circumstance of the wheel is 48 inches, how long is each spoke? Use 3.14 for and round your answer to the nearest hundredth.
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
Escape what is on sale for 60% off the regular $80 price what is the sales price
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
What is the answer to -282=-6(5+7x)
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
Solve using elimination
5x+3y=24
-2x-7y=-56
Answer:
Solution point (0,8)
Step-by-step explanation:
Multiply the top equation by 2
2*(5x + 3y = 24) Remove the brackets10x + 6y = 48 You could simplify this but don't.And multiply the bottom equation by 55*(-2x - 7y = -56)-10x - 35y = -280Now add the two equations together.
10x + 6y = 48 -10x -35y = - 280 The xs cancel out-29y = - 232 Divide by - 29y = -232/-29 Do the division y = 8=================
Solve for x
5x + 3y = 24 Substitute for y5x + 3*8 = 24 Combine on the left5x + 24 = 24 Subtract 24 from both sides 5x = 0 Divide by 5x = 0==================
This one is just a bit messier. I made a graph of it just to show that the answer is correct.
Divide fractions with thinking blocks
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)
Remy drinks 214 cups of water every 145 hours.
How many cups of water does he drink in 1 hour?
Enter your answer as a mixed number. For example, if your answer is 4212, enter 42 1/2
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
A population of bacteria increases by 30 every hour. Is this situation linear or exponential? A. Exponential, because the function grows by a common factor B. Exponential, because the function decreases C. Linear, because the function decreases D. Linear, because the function increases by a constant amount
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.
Explanation: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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Which of the following three dimensional objects has rotational symmetry about a line
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
Simplify the expression.
x^3/2/x^1/2
[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]
let f(x) = x^2 and g(x) = x − 3. evaluate (g ∘ f)(-2)
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
is there a proportional relationship between the area of an enlarged rectangle and the area of the original rectangle
Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65?
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%
What is the midpoint between z1 = -8 + 3i and z2 = 4 + 7i?
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.
if you flip a fair coin 6 times,what is the probability that you will get exactly 4 tails
The probability of getting exactly 4 tails when flipping a fair coin 6 times is 0.234375, or about 23.44%.
Explanation: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:
P(X=k) is the probability of getting k tails (in this case, k=4)n is the number of trials (in this case, n=6)p is the probability of getting a tail on a single trial (in this case, p=0.5)C(n, k) is the number of combinations of n things taken k at a time (in this case, C(6, 4) = 15)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%.
Find the distance between the points (5/2,3) and (3/2,8)
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
a cylinder has a volume of 72 inches. what is the volume of a cone with the same height and radius as the cylinder? Explain
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 volume of a cone is 24 in³.