Given:
It is given that,
PQ ⊥ PS and
∠QPR = 7x-9
∠RPS = 4x+22
To find the value of ∠QPR.
Formula
As per the given problem PR lies between PQ and PS,
So,
∠QPR+∠RPS = 90°
Now,
Putting the values of ∠RPS and ∠QPR we get,
[tex]7x-9+4x+22 = 90[/tex]
or, [tex]11x = 90-22+9[/tex]
or, [tex]11x = 77[/tex]
or, [tex]x = \frac{77}{11}[/tex]
or, [tex]x = 7[/tex]
Substituting the value of [tex]x = 7[/tex] in ∠QPR we get,
∠QPR = [tex]7(7)-9[/tex]
or, ∠QPR = [tex]40^\circ[/tex]
Hence,
The value of ∠QPR is 40°.
Ms. Baube launched a water balloon from the roof of the gym. Mr. Howard filmed the launch and gave her the data for the balloon's flight. How high was the roof of the school?
Answer:
I'd say 16 meters since that's the height when they started on the roof. I don't know where you got 25. That's the highest the balloon went.
The regular price of a computer was 739 dollars, but over the weekend it'll be on
sale for for 14 percent off. Which expression shows the difference in price from
normal(n) to sale?
A. n - 14
B. n - 1.14
C. nx 0.14
D. n - 0.14
Your answer here is
C. nx 0.14
After substituting, what is the first operation performed when evaluating 5+(9x-3)+2 for x = 5?
addition
multiplication
subtraction
division
Answer:
Multiplication
Step-by-step explanation:
Follow PEMDAS, so first you would sub in the 5 then work in the parentheses so you would multiply the 5
Which equation represents:
"An unknown integer, multiplied by the unknown integer minus a different unknown integer, equals 100."
A) x2 + xy + 100 = 0
B) x2 + xy − 100 = 0
C) x2 − xy + 100 = 0
D) x2 − xy − 100 = 0
Answer:
D) x² − xy − 100 = 0
Step-by-step explanation:
You want an expression for "An unknown integer, multiplied by the unknown integer minus a different unknown integer, equals 100."
SetupLet x represent the unknown integer, and y represent the different unknown integer. Their difference will be (x -y). When that is multiplied by x and the result equal to 100, we have ...
x(x -y) = 100
SimplifyEliminating parentheses using the distributive property, we have ...
x·x -x·y = 100
x² -xy = 100
Subtracting 100 gives an expression equal to zero:
x² -xy -100 = 0 . . . . . . . matches choice D
Question 1 (1 point)
Jackson created a model of one of the Great Pyramids shown below. What is the volume of the model?
6 cm
7 cm
8 cm
Answer: 112cm
Step-by-step explanation: to find the volume of a pyramid you do L*W*H/3 so if the dimensions are 6,7 and 8 all you have to do is multiply 6 by 7 ( thats 42) and then 42 times 8 (336) then divide by 3 which will get you 112.
Are the two spheres congruent?
no, because they have the same diameter length
no, because they have a different radius length
yes, because they appear to look the same size
yes, because they have the same volume
Answer:
The answer is B.
Step-by-step explanation:
B. No, because they have a different radius length.
The two spheres are not congruent because they have a different radius length.
What is Congruency?If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.
Given:
Sphere 1: Diameter = 12 cm
Sphere 2: Radius = 7 cm
The radius of Sphere 1 is 6 cm and sphere 2 is 7 cm and they are not equal.
Also, Volume of Sphere 1= 4/3 πr³
=904.32 cm³
and, Volume of Sphere 2 = 4/3 πr³
= 1,436.02 cm³
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The length of a basketball court is twice its
width. The perimeter is 150 feet. Find the
length and width of the basketball court.
Given:
The length of a basketball court is twice its width.
The perimeter of the perimeter is 150 feet.
To find the length and width of the basketball court.
Formula
The perimeter of the rectangle is
[tex]P = 2(l+b)[/tex]
where, l be the length of the rectangle and
b be the width of the rectangle.
Now,
As per the problem,
Let, the width be [tex]x[/tex], so the length be [tex]2x[/tex]
So,
The perimeter is = [tex]2(x+2x) = 6x[/tex]
According to the problem,
[tex]6x = 150\\or, x = \frac{150}{6}[/tex]
[tex]or, x = 25[/tex]
Therefore,
the width of the court is 25 ft and length = 2×25 = 50 ft
Hence,
The length and width of the basketball court is 50 ft and 25 ft respectively.
Final answer:
The width of the basketball court is 25 feet and the length is 50 feet.
Explanation:
Let's assume the width of the basketball court is 'x' feet. Since the length is twice the width, we can say the length is '2x' feet.
The perimeter of a rectangle is calculated by adding all of its sides. So, in this case, we have 2 lengths and 2 widths.
Perimeter = 2(length) + 2(width)
Given that the perimeter is 150 feet, we can write the equation: 150 = 2(2x) + 2(x)
Simplifying the equation, we get: 150 = 6x
Dividing both sides by 6, we find: x = 25
Therefore, the width of the basketball court is 25 feet and the length is 2x, which is 2 * 25 = 50 feet.
find the distance between -6 and 8
Answer:
14
Step-by-step explanation:
the distance between -6 and 8
6 + 8
= 14
Thus, the distance between -6 and 8 is 14
Any help? Will mark you as brainliest for the correct answer
Answer:
see explanation
Step-by-step explanation:
Given that 40 people liked cats, that is 20 women and 20 men
Then the dual bar representing 20 is made up of 4 frequency bars
Then each frequency bar represents 20 ÷ 4 = 5 people
Thus
dogs = 25 (men) + 30 (women) = 55
hamster = 15 ( men) + 5(women) = 20
other = 10(men) + 15(women) = 25
Favourite pet frequency table
favourite pet frequency
cat 40
dog 55
hamster 20
other 25
A total of 40 + 55 + 20 + 25 = 140
Roscoe traced around the bottom of a can to draw a circle. tell whether each statement about Roscoe 's circle is true. use 3.14 for pie
Answer with Step-by-step explanation:
a.If the circle has circumference of [tex]6\pi[/tex] in,then it has a diameter of 3 in.
Circumference of circle=[tex]6\pi[/tex]in
We know that
Circumference of circle=[tex]2\pi r[/tex]
Using the formula
[tex]6\pi=2\pi r[/tex]
[tex]r=\frac{6\pi}{2\pi}=3[/tex]in
Diameter of circle=[tex]2\times 3=6[/tex]in
It is false.
b.f the circle has diameter of 2 inches,then it has a circumference of 6.28 in.
Diameter,d=2 in
Circumference of circle=[tex]\pi d=3.14 \times 2=6.28[/tex]in
It is true.
c.If the circle has a circumference of [tex]2\pi[/tex]in then it has an area [tex]\pi[/tex] square inches.
Circumference=[tex]2\pi[/tex]in
[tex]2\pi r=2\pi[/tex]
[tex]r=\frac{2\pi}{2\pi}=1[/tex]in
Area of circle=[tex]\pi r^2=\pi(1)^2=\pi in^2[/tex]
It is true.
d.If the circle has a circumference of [tex]\pi[/tex]in then it has an area [tex]0.5\pi[/tex] square inches.
Circumference=[tex]\pi[/tex]in
[tex]2\pi r=\pi[/tex]
[tex]r=\frac{\pi}{2\pi}=\frac{1}{2}in[/tex]
Area of circle=[tex]\pi(\frac{1}{2})^2=0.25\pi in^2[/tex]
It is not true.
e.If the circle has a radius of 1.5 inches,then it has an area of 7.065 square inches.
Radius,r=1.5 in
Area of circle=[tex]3.14\times (1.5)^2=7.065in^2[/tex]
It is true.
Solve for x
Your answer must be simplified.
x/-6 ≥−20
Answer: x ≤ 120
Step-by-step explanation: To get x by itself in this inequality, since it's being divided by -6, we must multiply both sides by -6 just like we would if we were solving an equation.
But here is the trick you have to
watch out for with inequalities.
When you multiply or divide both sides of an inequality by a
negative, you must switch the direction of the inequality sign.
So our second step in this problem reads x ≤ 120.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when multiplying or dividing both sides of an inequality by a negative.
A student solved for the radius of a circle with a circumference of 12π. In which step did the student make an error?
Answer:
The student make an error in step 4.
Step-by-step explanation:
Given : A student solved for the radius of a circle with a circumference of 12π.
To find : In which step did the student make an error?
Solution :
Let us write each step to find the radius of a circle from its circumference
Step 1 - Circumference of circle,
[tex]C=2\pi r[/tex]
Step 2 - Substitute the given circumference,
[tex]12\pi= 2\pi r[/tex]
Step 3 - Divide both sides by 2π,
[tex]\frac{12\pi }{2\pi }=\frac{2\pi r}{2\pi }[/tex]
Step 4 - Solve
[tex]6=\pi r[/tex] , it is incorrect as π get cancelled
Correct step is [tex]6=r[/tex]
The radius of the circle is 6 cm.
Step 5 - [tex]\frac{6}{\pi }=\frac{\pi r}{\pi}[/tex]
Step 6 - [tex]\frac{6}{\pi }=r[/tex]
The student made a mistake in step 4 so step 5 and 6 is automatically invalid.
Therefore, the student make an error in step 4.
Solve for x
-8x = -48
x=-40
x=-6
x=6
x=-384
Answer:
Option C, x = 6
Step-by-step explanation:
Step 1: Divide both sides by -8
[tex]-8x = -48[/tex]
[tex]-8x / -8 = -48/-8[/tex]
[tex]x=6[/tex]
Answer: Option C, x = 6
Answer:
x = 6
Step-by-step explanation:
Let's solve your equation step-by-step.
−8x = −48
Step 1: Divide both sides by -8.
−8x /−8 = −48 /−8
x = 6
Find the common ratio of the geometric sequence
3/8, -3, 24, – 192,
Answer:
Common ratio = -8
Step-by-step explanation:
The common ratio of the geometric sequence will be - 8.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The geometric sequence is,
⇒ 3/8, -3, 24, - 192,
Now,
Since, The geometric sequence is,
⇒ 3/8, -3, 24, - 192,
Hence, The common ratio = Second term ÷ First term
= - 3 ÷ 3/8
= - 3 × 8/3
= - 8
Thus, The value of common ratio = - 8
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Mark is pitching a tent he ties a rope from a nail to the top of the tent what is the length of the rope between the nail and the top of the tent
6units
7units
12units
14units
Answer:
7 units
Step-by-step explanation:
solve for x
if you do ill give brainliest
Answer:
x = 9
Step-by-step explanation:
6² = 4·x
36 = 4x
x = 36/4
x = 9
Answer: x=9
X/6= 6/4
Crosses multiply
4x=36
Divide by 4
X=9
Step-by-step explanation:
What are the domain and range of f(x) = 2|x – 4|? domain: x <= 2; range: (-infinity,infinity) domain: (-infinity,infinity); range: f(x)>= 0 domain:(-infinity,infinity); range: f(x) <= 0 domain: x>= 2; range: (-infinity,infinity)
Answer:
domain: (-infinity,infinity);
range: f(x)>= 0
Step-by-step explanation:
f(x) = 2|x – 4|
The domain is the input values or the values that x can take
We can use any value we want for x
Domain: -infinity to infinity
The range is the output values
Since it is an absolute value, the smallest value it can take is 0, it can increase as large as it wants
Range: 0, infinity
what is the range and domain of a cube root function
Answer:
Domain: (-infinity, infinity), Range: (-infinity, infinity)
Step-by-step explanation:
This is an odd function. The graph passes through (0, 0), starting in Quadrant 3 and continuing into Quadrant 1.
There is a point on the graph for every input value, and so the domain of the cube function is (-infinity, infinity). Similarly, the range is (-infinity, infinity).
The range and domain of a cube root function are [0, ∞).
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
Cube root function is given as;
y = [tex]x^{1/3}[/tex]
Now as x increases (x > 0) y is also increasing although slower to x then still it is increasing.
So,
x → ∞ ⇒ y → ∞
For x < 0 it will become an imaginary number so it will not be defined.
Hence "The range and domain of a cube root function are [0, ∞)".
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A textbook store sold a combined total of 448 physics and biology textbooks in a week. The number of biology textbooks sold was 66 less than the number of physics textbooks sold. How many textbooks of each type were sold?
Answer:
Step-by-step explanation:
448 - 66 = 382
448 physics books and 382 biology books
what is the third step when calculating mean absolute deveation
Answer:
Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together. Step 4: Divide the sum by the number of data points.
Step-by-step explanation:
I need help with this worksheet
Answer:
look pal I will help I just need you to keep comening me
Can someone answer this question please? Thank u
Answer:
3) 3(5/12) = 5/4 hour = 1 1/4 hours
Find all constants α such that the vectors (α, 4) and (α, 5) are parallel.
Answer:
[tex]\alpha_{2} = \frac{5}{4}\cdot \alpha_{1}[/tex], for all [tex]\alpha_{1} \in \mathbb{R}[/tex]
Step-by-step explanation:
Vectors are parallel to each other if:
[tex]\vec u = \beta \cdot \vec v[/tex]
[tex](\alpha_{2}, 5) = (\beta\cdot \alpha_{1}, \beta \cdot 4)[/tex]
The value of [tex]\beta[/tex] is:
[tex]\beta = \frac{5}{4}[/tex]
Then, the following relationship is found:
[tex]\alpha_{2} = \frac{5}{4}\cdot \alpha_{1}[/tex], for all [tex]\alpha_{1} \in \mathbb{R}[/tex]
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,980 was collected on the sale of 1,236 tickets. How many of each type of ticket were sold?
Answer:
750 adult tickets
486 student tickets
Step-by-step explanation:
5 x 150=750 adult tickets
486 student tickets
Plz give brainliest need 1 more
Anybody can help me show the work on this problem ?
this is the explanation
Step-by-step explanation:
5x=75
22+5x=97
11y-5=106
7y+13=83
to conclude it all adds up to 360
360=83+106+97+75
PLEASE HELPP!!
Rachel is putting money into a savings account. She starts with $300 in the
savings account, and each week she adds $75.
Let S represent the total amount of money in the savings account (in
dollars), and let W represent the number of weeks Rachel has been adding
money.
a) Write an equation relating S to W.
b) Use the equation from part a to find the total amount of money in the
savings account after 16 weeks.
Answer:
A: s=75w
B: s= 75(16)
s=1200
Step-by-step explanation:
ax2 + bx + c
Factor the trinomial 7x2 – 3x – 4.
Which pair of numbers has a product of ac and a sum
of b?
ac
What is the factored form of the trinomial?
Answer: (7x + 4)(x - 1)
Step-by-step explanation:
7x^2 - 3x - 4
ax^2 = 7x^2
bx = -3x
c = - 4
4 x -7 = -28
4 + -7 = -3
4 and -7 are the number which ahs the product of ac = -28 and b = -3.
factored form : [tex]7x^{2} - 7x + 4x - 4[/tex]
= [tex]7x(x - 1) + 4(x - 1)[/tex]
= [tex](7x + 4)(x - 1)[/tex]
Answer:
1. -7 and 4
2. (7x + 4)(x - 1)
Will make brainliest if answered correctly
our family is driving to the beach. You travel 200 kilometers in the first two hours. During the next hour, you stop for lunch and only travel 25 kilometers. What was your average speed? *
Answer:
3.75Km
Step-by-step explanation:
to find Average speed you do distance over time so it would be 225/25=3.75
HELP PLEASE HELP I GIVE 10 POINTS
Answer:
The second one
Step-by-step explanation:
A linear function will always increase or decrease by the same amount:
The first one adds eight for every increase of 1 in the x value
The third one subtracts three for every increase of 1 in the x value
However,
The second one starts by adding three, and then adds 1.5 for the rest
The second table is nonlinear
100 points!!!Please help me I suck at math
Answer:
23 degrees
Step-by-step explanation:
We see that arc LM is 67 degrees. By definition, that means that the central angle <LPM also equals 67 degrees.
We also see that arc LMO is just a semicircle, which means that it is 180 degrees, by definition (because a whole circle is 360 degrees and a semicircle is just half a circle). In addition, angle MPN has that little square in its angle, which means that it is 90 degrees. By definition, its arc MN is also equal to 90 degrees. Then:
Arc LMO = arc LM + arc MN + arc ON
180 = 67 + 90 + arc ON
Solving, we get that arc ON = 180 - 67 - 90 = 23 degrees. By definition, that means the corresponding central angle <NPO is also equal to 23 degrees.
Notice that angles NPO and KPL are vertical angles, which means that by definition, they are equal in degree measure. So, since <NPO = 23, then <KPL = 23. Arc KL is the corresponding arc of <KPL, so by definition, arc KL is also 23 degrees.
Thus, the answer is 23 degrees.
Hope this helps!
Answer:
23°
Step-by-step explanation:
Angle KL = Angle MK - Angle ML
= 90 - 67
= 23