Answers
In a triangle, the total measure of all interior angles is 180 degrees. Since we have a right triangle here, one of the angles measures 90 degrees and the rest of the two angles when added must be 90 degrees as well.
So, we can say that 4x + (7x - 20) = 90 degrees.
Our next step here is to solve for x.
[tex]\begin{gathered} 4x+(7x-20)=90 \\ 4x+7x-20=90 \\ \text{Combine similar terms 4x and 7x.} \\ 11x-20=90 \\ \text{Add 20 on both sides.} \\ 11x-20+20=90+20 \\ 11x=110 \\ \text{Divide both sides by 11.} \\ \frac{11x}{11}=\frac{110}{11} \\ x\approx10 \end{gathered}[/tex]If x = 10, and measure of angle ABC is 4x, then 4(10) = 40 degrees.
The m∠ABC = 40 degrees. (Option B).
Related Questions
To demonstrate probabilities, a mathematics teacher had students draw cards from a bag which contained 26 red cards and26 black cards. During class, the bag was dropped, and 4 red cards and 2 black cards were lost.Tell whether the loss of cards changes the probability of drawing a black card from the bag.If so, was the probability increased or decreased? Support your answer by calculating the probability for each situation.
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The probability of an event is given by the following formula:
[tex]P(X)=\frac{Number\text{ of favorable outcomes to X}}{\text{Total number of possible outcomes}}[/tex]The total number of possible outcomes is the total number of red and black cards in the bag.
The favorable outcomes to drawing a black card in the first situation are 26 (because there are 26 black cards).
The probability of drawing a black card before the bag was dropped was:
[tex]P(\text{black card)=}\frac{26}{26+26}=\frac{26}{52}=0.5[/tex]After the bag was dropped, the total number of cards is:
Red cards= 26-4=22 and Black cards=26-2=24 cards.
Total number of cards=22+24=46.
The probability of drawing a black card after the bag was dropped is:
[tex]P(\text{black card)=}\frac{24}{46}=0.52[/tex]Thus, the probability of drawing a black card from the bag increased.
a) state the angle relationship write an equation & solve for the indicated variable and c) find the angle
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Notice that the given angles form a straight angle, therefore:
[tex](5x+4)^{\circ}+(x-2)^{\circ}+(3x+7)^{\circ}=180^{\circ}.[/tex]Then:
[tex]5x+4+x-2+3x+7=180.[/tex]Solving the above equation for x we get:
[tex]\begin{gathered} 9x+9=180, \\ 9x=180-9=171, \\ x=19. \end{gathered}[/tex]Answer: The angles are:
[tex]\begin{gathered} (5\cdot19+4)^{\circ}=99^{\circ}, \\ (19-2)^{\circ}=17^{\circ}, \\ (3\cdot19+7)=64^{\circ}. \end{gathered}[/tex]shade 1/5 of the gride what percent is equivalent to 1/5?
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Answer: 20%
Step-by-step explanation:
Find the surface area and volume of the larger solid.
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Solution
[tex]undefined[/tex]___%of 650 is 559 plss help
Answers
Answer:
86
Step-by-step explanation:
Answer:
86%
Step-by-step explanation:
hope u have a good day, and i should get many thanks for getting straight to the point and not leaving some long explanation that u won't use
Choose the correct letter in which the axis the point lies[ordered pair: (2.3, 2.5)]
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Hello!
To solve this exercise, we have to analyze the ordered pair:
(2.3, 2.5)Remember that we write an ordered pair as (x, y), so, this exercise says that x = 2.3 and y = 2.5, right?
So, at this moment we know that the two coordinates are positive, so this point will be in the first quadrant.
Right answer: alternative C.
Find the amount of time. I = $72, P = $600, r = 4%
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Answer:
3 years.
Explanation:
For a Principal (P) saved at simple interest, we use the formula below:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]Substituting the given values: I = $72, P = $600, r = 4%
[tex]72=\frac{600\times4\times T}{100}[/tex]We then solve for T (Time):
[tex]\begin{gathered} 600\times4\times T=72\times100 \\ T=\frac{72\times100}{600\times4} \\ T=3 \end{gathered}[/tex]The amount of time is 3 years.
A house bought for $70,000 was sold for $105.000.The selling price was what fraction of the purchase price (cost)? (Express As Fraction)
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The selling price was
C 0The midpoint of a segment can be found using the formulas for a directed line segment, x = ( 2 4 m )(x2 – x3] + xị andy=(a b]W2 - Yd) + y2. When using these formulas to find a midpoint, which is true?a = 1 and b = 2O a = 2 and b = 1O a = 1 and a + b = 2a = 2 and a + b = 2Mark this andenSave and ExitNexSubmit
Answers
We know that the mid point formula is
[tex]x=\frac{x_2+x_1}{2}\text{and y=}\frac{y_2+y_1}{2}[/tex]we will check one by one which option make this formula by substituing values given:-
It is given that
[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1and\text{ y=}\frac{a}{a+b}(y_2-y_1)+y_1[/tex]Now when a=1 anf b=2 we have
[tex]\begin{gathered} x=\frac{1}{3}(x_2-x_1)+x_1 \\ =\frac{x_2-x_1+3x_1}{3} \\ =\frac{x_2+2x_1}{3} \end{gathered}[/tex]which is not the midpoint formula
Now let's substitute a=1 and a+b=2
[tex]\begin{gathered} x=\frac{1}{2}(x_2-x_1)+x_1 \\ =\frac{x_2-x_1+2x_1}{2} \\ =\frac{x_2+x_1}{2} \\ \text{and } \\ y=\frac{1}{2}(y_2-y_1)+y_1 \\ =\frac{y_2-y_1+2y_1}{2} \\ =\frac{y_2+y_1}{2} \end{gathered}[/tex]which is the required formula.
Hence the correct option is a=1 , a+b=2
Need help with this number 3 and 4 all go together
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Solution:
Given:
[tex]\begin{gathered} m\angle3=65^0 \\ m\angle11=100^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle2+m\angle3=180^0.............the\text{ sum of angles on a straight line} \\ m\angle2+65^0=180^0 \\ m\angle2=180-65 \\ m\angle2=115^0 \end{gathered}[/tex]Therefore, the measure of angle 2 is 115 degrees.
[tex]\begin{gathered} m\angle5=m\angle11.........................(alternate\text{ exterior angles are congruent\rparen} \\ m\angle5=100^0 \end{gathered}[/tex]Therefore, the measure of angle 5 is 100 degrees.
[tex]\begin{gathered} m\angle13=m\angle3.........................(alternate\text{ interior angles are congruent\rparen} \\ m\angle13=65^0 \end{gathered}[/tex]
Therefore, the measure of angle 13 is 65 degrees.
25Sketch the graphs of the following equations.y=x+5, y =-(x+5), and y = x+5yer-
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Given the equations:
y = x+5
y = -(x+5)
y = |x+5|
The graphs of the given equations are:
ANSWER
y = x+5:
y = -(x+5):
y = |x+5|:
A vacuum cleaner dealership sold 390 units in 2011 and 407 in 2012. Find the percent increase or decrease in the number of units sold.
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Answer:
[tex]4.36\text{ \% increase}[/tex]Explanation:
Here, we want to get the percentage increase or decrease in the number of units sold
Since the number of units sold in 2012 is greater than the number of units sold in 2011, we have an increase
Mathematically, we can have the percentage increase or decrease as follows:
[tex]\begin{gathered} \frac{Number\text{ of units sold in 2012 - Number of units sold in 2011}}{\text{Number of units in 2011}}\text{ = } \\ \frac{407-390}{390}\text{ }\times\text{ 100 \%} \\ \\ =\text{ }\frac{17}{390}\times\text{ 100 \% = 4.36\%} \end{gathered}[/tex]Daisy is single with two children. Her income before deductions was $48,759. Her total deductions were $9,359. What is her adjusted income?
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Daisy adjusted income is $39,400
[tex]\begin{gathered} \text{Her adjusted income=48759-9359}=39400\text{dollars} \\ \end{gathered}[/tex]The following list gives the number of public libraries in each of 10 cities.4, 8, 3, 12, 2, 5, 11, 10, 7, 13Find the modes of this data set.If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
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Explanation
Given the data set
[tex]4,8,3,12,2,5,11,10,7,13[/tex]We are asked to find the mode of the dataset. This can be seen below.
Recall that the mode of a dataset is the number or set of numbers that appears the most in the dataset. By observation, we can see that each of the numbers in the data set occurs only once. Therefore, we can say that this implies that the data set has no mode.
Answer: No Mode
PLEASE HELP TIMED ASSIGNMENT PLATOwhat is the density of the oak board that is 5.5 inches wide, 1.5 inches thick and 3 feet long. show your work.Weight: 8.05 lbs
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The density is equal to the quotient between the weight and the volume of the board.
We can calculate the volume of the board as the volume of a rectangular prism: width by length by thickness.
[tex]V=w\cdot l\cdot t=5.5in\cdot(3ft\cdot\frac{12in}{1ft})\cdot1.5in=297\text{ cubic inches}[/tex]Then, if we divide the weight by the volume, we get:
[tex]\rho=\frac{W}{V}=\frac{8.05\text{ lbs}}{297\text{ in}^3}\approx0.027\frac{\text{ lbs}}{\text{ in}^3}[/tex]If we express the density in pounds per cubic feet, we can write:
[tex]\rho=\frac{W}{V}=\frac{8.05\text{ lbs}}{297\text{ in}^3}\cdot(\frac{12\text{ in}}{1\text{ ft}})^3=\frac{8.05\text{ lbs}}{297\text{ in}^3}\cdot\frac{1728\text{ in}^3}{1\text{ ft}^3}\approx46.84\frac{\text{ lbs}}{\text{ ft}^3}[/tex]Answer: the density is 46.84 pounds per cubic feet.
What is the function: f(x)=2x-9; translation 6 units up
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To translate any function vertically, we can add the units we want to translate to the function. If the tranlation is up, we add a positive value, if it is down, we add a negative value.
We want 6 units up, so we put a "+ 6" in f(x):
[tex]f(x)+6=2x-9+6=2x-3[/tex]So, the function after translation is:
[tex]f(x)=2x-3[/tex]Cards are drawn from a well-shuffled deck of 52. Find the probability for each event below. a) Drawing a King or a heart. b)Drawing a Jack or a seven. c)Drawing a Jack and a seven.
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We know that the probability is given by:
[tex]P=\frac{\text{ number of favorable outcomes}}{\text{ total number of possible outcomes}}[/tex]a)
Since a standard deck has 4 different suits this means that each one of them has 13 cards. Then we have 13 hearts, a standard deck has a total of 4 kings, since one of them is from the heart suit this means that in total we have 16 favorable outcomes. Hence the probability for this case is:
[tex]P=\frac{16}{52}=\frac{4}{13}[/tex]Therefore, the probability of drawing a king or a heart is 4/13
b)
In this case we have 4 possible outcomes for the jack and 4 possible outcomes for the seven, this means that in total we have 8 favorable outcomes, hence:
[tex]P=\frac{8}{52}=\frac{2}{13}[/tex]Therefore, the probability of drawing a jak or a seven is 2/13.
c)
In this case we have two different possibilities: A probability if we replace the first card drawn and a probability if we don't replace the first card drawn.
With replacement:
We know that we have 4 favorable outcomes for each drawn, to find the probability of getting both of the cards we want we need to multiply them, hence:
[tex]P=\frac{4}{52}\cdot\frac{4}{52}=\frac{1}{13}\cdot\frac{1}{13}=\frac{1}{169}[/tex]Therefore, the probability of getting a Jack and a seven with replacement is 1/169
Without replacent:
In this case we have a probability of 4/52 to get a jack (or a seven) in the first draw; for the second draw we have one card less in total in the deck this means that we have a probability of 4/51 of getting a seven (or a jack if the first one was seven). Hence the probability is:
[tex]P=\frac{4}{52}\cdot\frac{4}{51}=\frac{1}{13}\cdot\frac{4}{51}=\frac{4}{663}[/tex]Therefore, the probability of getting a jack and a seven without replacement is 4/663
I need help with these textbook problems #12 and #13
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We will have the following:
12. The zeros we can see are located at:
[tex]\begin{gathered} (2-x)(3-2x)=0 \\ \\ \Rightarrow2-x=0\Rightarrow x=2 \\ \\ and \\ \\ \Rightarrow3-2x=0\Rightarrow2x=3\Rightarrow x=\frac{3}{2} \end{gathered}[/tex][tex]\begin{gathered} x=2 \\ \\ x=\frac{3}{2} \end{gathered}[/tex]13. We determine the zeros as follows:
[tex]\begin{gathered} f(x)=9x^2+6x+1\Rightarrow f^{\prime}(x)=18x+6=0 \\ \\ \Rightarrow18x=-6\Rightarrow x=-\frac{1}{3} \end{gathered}[/tex]So, there is only one zero at:
[tex]x=-\frac{1}{3}[/tex]are the two triangles similar? If yes, then complete the similarity statement. Select all that apply
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The distance from the centre of a circle to a point P outside the circle is 12 mm. The length of the tangent segment from P to the circle is 9 mm. Determine the radius of the circle.
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This is a right angled triangle;
Using pythagoras theorem, we have;
[tex]\begin{gathered} r=\sqrt{12^2-9^2} \\ r=3\sqrt{7}=7.94mm \end{gathered}[/tex]Thus, the radius is 7.94mm
How many fence material is needed to make a dog pen which measures 10ft by 10ft and is 6ft high
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Answer:
240 ft²
Explanation:
The number of square feet needed is equal to the lateral surface. So, it can be calculated as:
[tex]A=2(l+w)h[/tex]Where l is the length, w is the width and h is the height.
Then, replacing l by 10 ft, w by 10 ft, and h by 6ft, we get:
[tex]\begin{gathered} A=2(10+10)\cdot6 \\ A=2(20)\cdot6 \\ A=40\cdot6 \\ A=240 \end{gathered}[/tex]Therefore, the answer 240 ft²
if g(x)=x^2-x, find g(2)
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Substitute 2 for x in the equation g(x)=x^2-x to obtain the value of g(2).
[tex]\begin{gathered} g(2)=2^2-2 \\ =4-2 \\ =2 \end{gathered}[/tex]So value of g(2) is 2,
Find the slope of the line given the following two points:
(-2, 6) and (4, -3)
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The slope of the line is m = -3/2.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).So, obtain the slope as:
Slope formula: m = y₁ - y₂/x₁ - x₂Substitute the values in the formula and solve as follows:
m = y₁ - y₂/x₁ - x₂m = 6 -(-3)/-2 - 4m = 6 + 3/-6m = 9/-6m = -3/2Therefore, the slope of the line is m = -3/2.
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need help figuring this out I think the answer is 30.
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Note that the sum of the angles in a triangle is always 180 degrees
angle A + angle B + angle C = 180
From the given problem :
angle A = 60
angle C = 90
using the formula above :
60 + angle B + 90 = 180
angle B = 180 - 150
angle B = 30
Therefore the unknown angle is 30 degrees
What is the cost per mile to ride in the taxi?
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Given:-
[tex]C=2.25+0.85m[/tex]To find:-
Cost per mile.
So per mile means 1 mile. so now we substitute the value of m as 1. we get,
[tex]\begin{gathered} C=2.25+0.85(1) \\ C=2.25+0.85 \\ C=3.10 \end{gathered}[/tex]So the required solution is $3.10
Which sequence of transformation could be applied to pentagon J to create pentagon K
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In general, the formula for a clockwise/counterclockwise 90° rotation is
[tex]\begin{gathered} (x,y)\to(-y,x)\to\text{counterclockwise} \\ (x,y)\to(y,-x)\to\text{ clockwise} \end{gathered}[/tex]In our case, since point (-1,6) is on figure J,
[tex]undefined[/tex]A company manufactures aluminum mailboxes in the shape of a box with a half cylinder top. The company will make 1452 mailboxes this week if each mailbox has dimensions not shown in the figure below how many square meters of aluminum will be needed to make these mailboxes in your calculations. Use the value 3.14 for pi and round up your answer to the next square meter.
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Applying the formula for the surface area of a box and a cylinder, the amount of aluminum needed is approximately: 817 m².
What is the Surface Area of a Box and the Surface Area of a Cylinder?The surface area of a box = 2(l*w + l*h + w*h), where:
h = height of the boxl = lengthw = width of the box.The surface area of a cylinder = 2πr(h + r), where:
h = height of the cylinderr = radius of the cylinderThus, the material needed for one mailbox = (surface area of a box + 1/2 of surface area of a cylinder) - area of the surface both share
= [2(l*w + l*h + w*h) + 1/2(2πr(h + r))] - 2(l*w)
The variables are:
l = 0.45 m
w = 0.2 m
h = 0.3 m
r = 1/2(0.2) = 0.1 m
h = 0.45 m
Substitute the values into the equation:
Surface area of one mailbox = [2(0.45*0.2 + 0.45*0.3 + 0.2*0.3) + 1/2(2*3.14*0.1(0.45 + 0.1))] - 2(0.45*0.2)
Surface area of one mailbox = [0.57 + 0.1727] - 0.18
Surface area of one mailbox = 0.5627 m²
Aluminum needed = surface area of 1452 mailboxes = 1452 × 0.5627 ≈ 817 m²
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given the following matrices, if possible, determine 4A. if not, state “not possible”
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Recall that the product of a scalar and a matrix A is a matrix with entries equal to the product of the scalar and the value in that entry matrix A.
Therefore:
[tex]4A=4\begin{bmatrix}-3{} & {}-4 & {} \\ {-3} & -5 & {} \\ {6} & {-7} & {}\end{bmatrix}=\begin{bmatrix}-3\times4{} & {}-4\times4 & {} \\ {-3}\times4 & -5\times4 & {} \\ {4\times6} & {-7}\times4 & {}\end{bmatrix}\text{.}[/tex]Simplifying the above matrix we get:
[tex]4A=\begin{bmatrix}-12{} & {}-16 & {} \\ {-12} & -20 & {} \\ {24} & {-28} & {}\end{bmatrix}\text{.}[/tex]Answer:
[tex]4A=\begin{bmatrix}-12{} & {}-16 & {} \\ {-12} & -20 & {} \\ {24} & {-28} & {}\end{bmatrix}\text{.}[/tex]the cost of a car rental is 30$ per day plus 19c per mile. you are on a daily budget of $87. write and shovel an inequality to find the greatest distance you can drive each day while staying within your budget.
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ANSWER:
[tex]\begin{gathered} 30+0.19x\le87 \\ x\le300 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We know that a penny is equal to 0.01 dollar, which means that we can establish the following equality:
[tex]\begin{gathered} 30+0.19x\le87 \\ \text{where x are the miles driven} \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 0.19x\le87-30 \\ x\le\frac{57}{0.19} \\ x\le300 \end{gathered}[/tex]300 miles is the maximum for the $ 87 budget
The next model of a sport car will cost 4.1% less than the current model the current model cost $48,000 how much will the price decrease in dollars? What will be the price of the next model?
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Given that the next model of a sports car will cost 4.1% less than the current model cost $48,000.
The price decrease in dollars = 4.1% of $ 48000
[tex]=\frac{4.1}{100}\times48000[/tex][tex]=1968\text{ }[/tex]The price decrease in dollars = $ 1968.
The price of the next model =$48000-1968
The price of the next model = $ 46,032.
