Answer:
X = 14
Hope this helps!
Step-by-step explanation:
The small red square means the angle is 90°.
( 2x + 22 ) + ( 3x - 2 ) = 90°
2x + 22 + 3x - 2 = 90
( 2x + 3x ) + ( 22 - 2 ) = 90
5x + 20 = 90
5x + 20 - 20 = 90 - 20
5x = 70
x = 14
Answer: x = 14
Step-by-step explanation:
When you have a right angle, they add up to 90 degrees
So you add up the two angles that you have that equal a total of 90 degrees
2x+22 + 3x-2 = 90
5x+20 = 90
5x = 70
x = 14
I hope this helps :D
2x+2y=-22
5x +6y = -63
Answer:
Step-by-step explanation:
Find an equation to represent x or y
2x + 2y = -22
-2y
2x = -22 - 2y
Divide by 2
x = -11 -y
Plug in the found equation
5 (-11 - y) +6y = - 63
- 55 -5y + 6y = - 63
-55 + y = - 63
+55
y = - 8
Plug in the y to find x
2x + 2(- 8) = - 22
2x - 16 = - 22
+ 16
2x = - 6
Divide by 2
x = - 3
The length of segment AE is 5 centimeters. a. what is the length of segment CD? b. what is the length of segment AB? c. Name a segment that had the same length ...
a) The length of segment CD is; CD = 10 cm
b) The length of segment AB is; AB = 5 cm
c) Another segment with same length as segment AB is;
Segment AC
What is the length of the line segment?From the attached image, we see that Segment AE is a radius of the circle with center of A.
Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.
a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.
Diameter = 2 × radius.
Diameter; CD = 2 × AE
CD = 2 × 5
CD = 10 cm
b) AB is a radius as defined earlier and as such; AB = AE
Thus; AB = 5 cm
c) The other segments that are also radius of the circle and have the same length as segment AB are;
Segment AC
Segment AD
Segment AG
Segment FA
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How do i graph this? 4x - 2y > 12
Step-by-step explanation:
X-intercept is where the line crosses the x-axis or where y = 0
So, put y = 0 in the given equation
4x + 2(0) = 12
4x = 12
x = 12/4
x = 3
What is the equation of the line that passes through the points (-7.
-5) and (2, 3)? Write your answer in slope-intercept form.
Show your work here
The equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
The first point = (-7, -5)
The second point = (2, 3)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (3- (-5) / (2 - (-7))
= (3 + 5) / (2 + 7)
= 8 / 9
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point = (2,3)
Substitute the values in the equation
y - 3 = (8/9)(x - 2)
y - 3 = (8/9)x - 16/9
y = (8/9)x - 16/9 + 3
y = (8/9)x - 11/9
Hence, the equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
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Mr.Hollis determines that he gives away 800each month if he gives away 16 of his budget then how much is his overall budget
The overall budget the Mr Hollis has is $12800.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Mr.Hollis determines that he gives away 800 each month and the fraction is 1/6 of his budget.
The value of the overall budget will be illustrated as x.
Therefore 1/16 × x = 800
x / 16 = 800
x = 16 × 800
x = 12800
Hollis has $12800 as budget.
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Question 11-(3 marks available)
Find the total surface area of this triangular prism.
13 cm
5 cm
12 cm
9 cm
20 cm
Answer: 1080 [tex]cm^{2}[/tex]
Determine the values of b1, b2, and b3, the sides of the triangular base. Also determine the value of h, the height of the triangular base and l, the length of the prism (the length between the bases).
The sides of the triangular base are:
b1 = 13 in.
b2 = 14 in.
b3 = 15 in.
The triangular base is a right triangle, and so the height is one of our sides. We will use
h = 12 in.
The length of the prism is
l = 20 in.
total surface area = bh + (b1+b2+b3)*l
bh = 12*20 = 240 [tex]cm^{2}[/tex]
l * (b1+b2+b3) = 20*(13 + 14+ 15) = 840 [tex]cm^{2}[/tex]
TSA = bh + l * (b1 + b2 + b3) = 240 + 840 = 1080 [tex]cm^{2}[/tex]
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Calculate S16 for the arithmetic sequence defined by (an) = {5/8-5/16n}
65/
2
65/
8
-65/
8
-65/
2
The sum of the first 16 terms of the defined arithmetic sequence is given as follows:
-520/16.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the equation presented as follows, called general equation:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the arithmetic sequence.
The sum of the first n terms is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The sequence in this problem is defined as follows:
[tex]a_n = \frac{5}{8} - \frac{5}{16}n[/tex]
The first term is of:
[tex]a_1 = \frac{5}{8} - \frac{5}{16} = \frac{5}{16}[/tex]
Hence the 16th term of the sequence is of:
[tex]a_{16} = \frac{5}{8} - \frac{5}{16}(16) = \frac{5}{8} - 5 = -\frac{35}{8}[/tex]
Hence the sum of the first 16 terms of the arithmetic sequence is defined as follows:
[tex]S_{16} = 8\left(\frac{5}{16} - \frac{35}{8}\right) = 8 \times \left(-\frac{65}{16}\right) = -\frac{520}{16}[/tex]
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30 point reward if you help ! find the volume of each shape and then compare. do not reduce your fractions.
The volume of the cuboid is [tex]\frac{6}{125}[/tex] and The volume of the cube is [tex]\frac{8}{27}[/tex]
The comparison of both a cube and a cuboid have six faces,a cube has six faces which are all squares and on the other hand, the cuboid is but a cuboid has rectangular faces.
What is a Cube?
A cube is a symmetrical three-dimensional shape which has all six sides equal.
To find the volume of cube is addition of all seen sides or the given sides all squared.
i.e volume of a cube= [tex]a^{3}[/tex]
volume of the cube=([tex]\frac{2}{3}[/tex])^3
Volume= [tex]\frac{8}{27}[/tex] cubic inches
How to dertermine the volume of a cuboid
Whar is a Cuboid?
A Cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges which the volume can be measured by multiplying the length by the breadth by the height .
Volume of a cuboid = L×B×H
Volume of a cuboid=[tex]\frac{2}{3}[/tex]×[tex]\frac{1}{5}[/tex]×[tex]\frac{3}{5}[/tex]
Volume of a cuboid=[tex]\frac{6}{125}[/tex] cubic inches.
To compare,
A cube has shapes of equal sides six faces and a cuboid faces are non-equal with six faces, 8 vertices and 12 edges.
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Find a1 if d = -2 and a21 = 18.
The answer is either 58 or 60
For the given values of the arithmetic sequence d = -2 , a₂₁ = 18,then the value of a₁ = 58.
As given in the question,
Given values of the arithmetic sequence :
Common difference 'd' = -2
Twenty first term a₂₁ = 18
Formula for the nth term of arithmetic sequence with common difference 'd' and first term a₁ is given by:
aₙ = a₁ + (n -1) d
Substitute the value n =21 , a₂₁ =18 and d = -2 in the above equation we get,
⇒a₂₁ = a₁ + (21 -1)(-2)
⇒18 = a₁ + 20(-2)
⇒ a₁ = 18 +40
⇒a₁ = 58
Therefore, for the given values of the arithmetic sequence d = -2 ,
a₂₁ = 18,then the value of a₁ = 58.
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Question 10 of 10
Which of the following is the solution to | x | +5 ≤1?
OA. No solution
OB. xs-4
C. All values are solutions *
OD. xs-4 and x ≥ −6
The solution of | x | +5 ≤ 1 is option C, All values are solutions
We need to find the solution of | x | +5 ≤ 1
Upon removing the modulus function, the term presnet within it can be either negative or positive
considering it as postive
| x | +5 ≤ 1
x + 5 ≤ 1
x ≤ 1 - 5
x ≤ -4
considering it as negative
| x | +5 ≤ 1
-x + 5 ≤ 1
-x ≤ 1 - 5
-x ≤ -4
x ≥ -4
Therefore, the solution of | x | +5 ≤ 1 is All values are solutions
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How can you earn a high credit score?
A. After ten years of never making any payments or having loans.
B. After you have made your first credit card payment.
C. When you turn thirty years old.
D. Over time by paying off your loans and making payments on time.
Answer:
The correct answer is D because Option A won't work neither will option B because a long credit history will help ur credit score, C isn't right either
What are the coordinates of the vertices after a rotation 90 counterclockwise around the origin.
Answer:When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Step-by-step explanation: trust me
50 points!!! Are rational functions and hyperbolas the same? Please explain why or why not.
Complete the statement to describe the expression (a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains terms
The statement about the given expression is described below.
What is expression?A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.
According to given data:Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2
It has factors two which consist of 3 termsEach factor has a multiplicity of 2terms in factor (a+b+c) are a, b, cTerms in factor (d+e+f) are d, e, fThus, given expression has two factors which consist 3 terms.
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On September 16th you bought 2,500 shares of the stock you have chosen to follow this year,
along with 1,100 shares of Home Depot, 3,500 shares of Ford, and 900 shares of JetBlue.
Create a stock ticker to represent these trades.
The stock markets utilize "Ticker Symbols," which are distinctive one- to five-letter codes, to uniquely identify companies.Because stock quotes used to be printed on a ticker tape machine that resembled the images below, it is known as a ticker symbol.
Create a stock ticker to represent these trades ?A tracking stock is unique equity offered and issued by a parent company that tracts the financial performance of a segment of the division.Tracking stocks usually trade in open markets separate from the parent company's stock.An example of tracking stock is:Walt Disney Company's subsidiary which it owns fully named: go.com. The company is also known as The Go Network. The stock symbol is GOT.Its P/E Ratio is 11.38XI chose this stock because its parent company has a very strong brand and great leadership.Price/Earnings Ratio is used for establishing the value of a company. It measures the current share price against it's earnings per share (EPS).To learn more about stock ticker refer
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a manufacturing machine has a 5% defect rate. if 7 items are chosen at random, what is the probability that at least one will have a defect?
The probability of selecting at least one defective item at random is 0.3017.
The probability of an event occurring at least once will be calculated as the complement of the probability of the event never occurring. You can use exponents to multiply the number of events that occurred when calculating this amount.
Defect rate = P(defect) = 0.05
Probability is defined as the required outcome divided by the total number of possible outcomes.
P( at least 1 is defective) = 1 - P(none is defective)
P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95
P(none is defective) = P(non defective)^7
P(none defective) = 0.95× 0.95 × 0.95 × 0.95 × 0.95× 0.95× 0.95=0.6983
P(at least one is defective) = 1 - 0.6983 = 0.3017
Therefore, probability of at least one defective item is 0.3017.
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Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
The equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
According to the question,
We have the following information:
Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
Now, we have the following arithmetic progression with common difference, denoted by d:
22, 22.5, 23, 23.5, ...
Formula used to find the nth term:
an = a+(n-1)d where a is the first term
A) 22+(d-1)0.5 = 30
B) The plant still have to grow 8 cm because the difference between 30 and 22 is 8 cm.
C) Value of d:
22+(d-1)0.5 = 30
22+0.5d-0.5 = 30
21.5+0.5d = 30
0.5d = 30-21.5
0.5d = 8.5
d = 8.5/0.5
d = 17
Hence, the equation that can be used to solve for the number of days until the plant has a height of 30 cm is 22+(d-1)0.5 = 30 where d represents the number of days and the value of d is 17.
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Can someone help me on this question? I think it’s the 2nd choice but I’m not sure
Answer:
5√3
Step-by-step explanation:
There are two triangles shown in the image.
First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.
The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.
In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.
This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.
x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.
-3(4x-7) please answer quickly!!
Consider the equation 2x^(2)+2y^(2)+2x-2y-7-0 Write the equation in the standard form of a circle? What is the center and the radius
Solve this equation:
11x^2=-8
Answer:
See below
Step-by-step explanation:
11x^2 = - 8
x^2 = - 8/11
x = + - i sqrt (8/11) or - .727 i or .727 i
Find the range for the measure of the third side of a
triangle given the measures of two sides.
8, 13
By using properties of triangle, it can be inferred that
The value of c lies between 5 and 21 and also 5 and 21 are not included
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°
Let a = 8, b = 13 and let the third side be c
We know sum of two sides of a triangle is always greater than the third side
a < b + c
8 < 13 + c
c > 8 - 13
c > -5, which is obvious
b < c + a
13 < c + 8
c > 13 - 8
c > 5
c < a + b
c < 8 + 13
c < 21
5 < c < 21
The value of c lies between 5 and 21 and also 5 and 21 are not included
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solve for x 4{x+1 1/3]=9 2/3
The solution for the expression is X =87/ 48 or 1.812
To solve for x in the equation we follow the step below:
Step 1: Open the bracket by multiply 4
= 4x +4x/3 = 9 2/3
= 4x + 4x /3 = 29/3
Step 2: Evaluate for X
= [tex]\frac{12x + 4x}{3}[/tex] = [tex]\frac{29}{3}[/tex]
= [tex]\frac{16x}{3}[/tex] =[tex]\frac{29}{3}[/tex]
Step 3: Cross multiply
: 3 (16x) = 3(29)
48x = 87
Step 3: Divide both sides by 48
=[tex]\frac{48x}{48}[/tex] =[tex]\frac{87}{48}[/tex]
x = [tex]\frac{87}{48}[/tex] = 1.812
Therefore, the solution for the expression is X =87/ 48 or 1.812
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when looking at the results of a 99% confidence interval, we can predict what the results of the two-sided significance test will be:
0.01 is the results of the two-sided significance test in confidence interval,
What is alpha in statistics?
A test statistic's statistical significance is determined by its alpha value. The researcher selects it. In a statistical test, the probability of a Type I error is represented by alpha. Considering that alpha is a probability, its range is 0 to 1.confidence level = 1 - alpha
so alpha = 1 - confidence level = 1 - 0.99 = 0.01
In statistics, alpha is the number that evaluates the test statistic to see if it is significant or not. In other words, alpha is the allowable type 1 error margin. The significance level, or alpha, is the antithesis of the confidence level. Confusion level + significance level = 1.
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Can anyone write the equation of the graph?
The equation of the absolute function graph given in the diagram is: y = |x - 3| + 5.
How to Find the Equation of the Graph of an Absolute Value Function?y = a|x – h| + k is the equation, in vertex form, that represents the absolute value function where:
The vertex of the graph of the absolute value function = (h, k) The graph opens up or opens down depends on the value of a.The vertex of the graph is (3, 5). This implies that:
(h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation in vertex form, y = a|x – h| + k:
y = a|x – h| + k
y = a|x - 3| + 5
To find the value of a, substitute a point on the graph, (5, 7), into the y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 - 5 = 2a [subtraction property]
2 = 2a
a = 1 [division property of equality]
Substitute a = 1 into the equation y = a|x - 3| + 5:
y = |x - 3| + 5
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6) In Jim’s school, there are 3 girls for every 2 boys. There are 800 students in total. Using this information, how many students are girls?
A. 260
B. 320
C. 480
D. 390
Answer:
C) 480
Step-by-step explanation:
Ratio:
[tex]\sf \dfrac{3}{5}*800 = 3 * 160[/tex]
= 480
Select the correct answer.
What is the domain of function f?
D
Step-by-step explanation:
The domain is the X-values in your function
as you can see, the X values continue to increase as the lines continue, infinitely
a bank wishes to estimate the mean credit card balance owed by its customers. the population standard deviation is estimated to be $300. if a 98% confidence interval is used and an margin of error of $75 is desired, how many customers should be sampled?
Using a 98% confidence interval, the total number of customers that should be sampled is 87.
What exactly is sample size?The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.
Given,
Standard deviation σ=300
Confidence level: 0.98
Maximum allowable error: ε=75
The critical value is calculated using the standard normal table at the level of significance (0.02)
The critical value in this case is 2.326.
Sample size is calculated by,
n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²
n=((2.326)²×(300)²)/(75)²
n=86.564≈87
Therefore, the required sample size is 87.
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Write2 1/4 as an improper fraction in its simplest form
Answer:
9/4
Step-by-step explanation:
Mr. Young is replacing the fencing around his rabbit pens and garden. The table shows the dimensions of the different areas.
Item
Length
(ft)
Width
(ft)
Rabbit Pen 3.5 4.5
Garden 12 10
How many feet of fencing will he need to replace two rabbit pens and his garden? The perimeter of a rectangle is 2ℓ+2w
2
ℓ
+
2
w
, where ℓ is the length and w is the width.
__ ft
Total fenced need to replaced is 60 feet
What is Perimeter of rectangle?The Perimeter of rectangle is two times the sum length and width.
i.e., Perimeter of rectangle= 2( l+ w)
Given:
Rabbit Pen: Length= 3.5, width= 4.5
Garden: length= 12, width = 10
So, Perimeter of Rabbit Pen = 2( 3.5 + 4.5)
= 2( 8)
= 16 feet
Now, Perimeter of Garden = 2 (12 + 10)
= 2( 22)
= 44 feet.
Total fenced need to replaces= 16 +44 = 60 feet
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Answer:
Step-by-step explanation:
76