Consider the diagram and angle measures shown below.m∠1 = (3x +25)m∠2 = (7x+5)m∠3 =(-2x + 70)4322 || 7What is the value of m∠3 ?
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First, we need to find the value of x
m<4 = m<1 = (3x + 25)° ( corresponding angle)
Let the angle between m<2 and m<3 be m<5
m< 5 = m<4 = (3x + 25)° ( vertical angle)
m<2 + m<5 + m<3 = 180° (angles on a straight line
(7x+5)° + (3x+25)° + (-2x + 70)° = 180°
7x + 5 + 3x + 25 -2x + 70 = 180
Rearrange
7x + 3x -2x + 5 + 25 + 70 = 180
8x + 100 = 180
subtract 100 from both-side of the equation
8x = 180 - 100
8x = 80
Divide both-side of the equation by 8
x = 10
m<3 = -2x + 70
substitute x = 10 in the above
m<3 = -2(10) + 70 = -20 + 70 = 50°
Related Questions
12. Make an estimate and then divide as if the dividend was a whole number. Use the estimate to place your decimal.8.46 ➗3=Estimate: What partial quotients did you use? ___how to divide 3 into 8.46 dividing decimals?______________________Answer:
Answers
Given data:
The given expression is 8.46 ➗3.
The given expression can be written as,
Thus, the quotient is 2.82 which is in decimal.
Point A is located at (2, 6), and point M is located at (−1, 8). If point M is the midpoint of segment AB, find the location of point B. a(5, 4) b(0.5, 7) c(0, 6) d(−4, 10)
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ANSWER:
d. (−4, 10)
STEP-BY-STEP EXPLANATION:
The midpoint has the following definition:
[tex]\left(x_m,y_m\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)[/tex]We can calculate point B, using the following equations obtained taking into account the above:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ \\ -1=\frac{2+x_2}{2} \\ \\ x_2+2=-2 \\ \\ x_2=-2-2=-4 \\ \\ \\ y_m=\frac{y_1+y_2}{2} \\ \\ 8=\frac{6+y_2}{2} \\ \\ y_2+6=16 \\ \\ y_2=16-6=10 \\ \\ \text{ Therefore, point B is located at \lparen-4, 10\rparen} \end{gathered}[/tex]The correct answer is: d. (−4, 10)
a) Form a suitable equation to show that x squared - 6x - 59 = 0b) Complete the square (x+p)squared-q= 0, and find the constants p and q.
Answers
Given:
There is a triangle given as
Required:
We want to find the sutiable form that show that
[tex]x^2+6x-59=0[/tex]and also complete the square
[tex](x+p)^2-q=0[/tex]and find the value of p and q
Explanation:
The area of triangle is
[tex]\begin{gathered} \frac{1}{2}(x+1)(x+5)=32 \\ \\ x^2+5x+x+5=64 \\ x^2+6x-59=0 \end{gathered}[/tex]hence proved for a
Now for second
[tex]\begin{gathered} x^2+6x+9-9-59=0 \\ (x+3)^2-68=0 \end{gathered}[/tex]now compare with
[tex](x+p)^2-q=0[/tex]we get
[tex]\begin{gathered} p=3 \\ q=68 \end{gathered}[/tex]Final answer:
p=3 and q=68
Savannah earned a score of 720 on Exam A that had a mean of 700 and a standarddeviation of 25. She is about to take Exam B that has a mean of 400 and a standarddeviation of 100. How well must Savannah score on Exam B in order to doequivalently well as she did on Exam A? Assume that scores on each exam arenormally distributed.
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Answer:
480
Explanation:
First, we need to standardize the score on Exam A. It can standardize as
[tex]z=\frac{\text{ score}-\text{ mean}}{\text{ standard deviation}}[/tex]Replacing score = 720, mean = 700, and standard deviation = 25, we get
[tex]z=\frac{720-700}{25}=\frac{20}{25}=0.8[/tex]Then, to do equivalently well on exam B, we need a standard value equal to 0.8. So, the score can be calculated as
[tex]\text{ score = z\lparen standard deviation\rparen + mean}[/tex]Replacing z = 0.8, standard deviation = 100 and mean = 400, we get
[tex]\begin{gathered} \text{ score = 0.8\lparen100\rparen+400} \\ \text{ score = 80 + 400} \\ \text{ score = 480} \end{gathered}[/tex]Therefore, the answer is 480
3) Graph y=-3 (x - 2)2 + 3
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The equation is:
[tex]y=-3(x-2)^2+3[/tex]So this is a parabola, so we can graph it with the vertex and the intercections with the x axis
So the vertex is in the coordinat (2,3) becuase of the transformation of -2 in the x axis and +3 in the y axis so the vertex is (2, 3)
now for the interception with the x axis we replace y = 0 and solve for x so
[tex]0=-3(x-2)^2+3[/tex]we open the parenthesis like:
[tex]undefined[/tex]Rewrite each of the following expressions so that they have no division
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Using the law of indices,
[tex]\frac{1}{x^6}[/tex]will be
[tex]\frac{1}{x^6}=x^{-6}[/tex]Evaluate 2(x-1), if x= -3
Answers
To evaluate the expression for x = -3, we simply put in -3 whereever we see x in the expression.
Doing this gives us
[tex]2(x-1)\rightarrow2(-3-1)[/tex]We now simplify the expression on the right
[tex]=2(-4)[/tex][tex]=-8[/tex]which is our answer!
You have $10,000 in a savings account. You want to take most of the money out and invest it in stocks and bonds. You decide to invest nine times as much as you leave in the account. You also decide to invest five times as much in stocks as in bonds. How much will you invest in stocks, how much in bonds, and how much will youleave in savings?
Answers
Answer:
7,500 in stocks
1,500 in bonds
1,000 in savings
Explanation:
First, let's call x the quantity that you will leave in saving and y the quantity that you will invest in stocks and z the quantity that you will invest in bonds.
Now, we can formulate the following equations:
x + y + z = 10,000
y + z = 9x
y = 5z
Because you have 10,000 in savings, you decide to invest nine times as much as you leave in the account, and you also decide to invest five times as much in stocks as in bonds.
So, we can rewrite the expressions as:
x + y + z = 10,000
-9x + y + z = 0
y - 5z = 0
Now, we can multiply the second equation by -1 and sum this equation with the first one as:
-9x + y + z = 0
(-9x + y + z)*(-1) = 0*(-1)
9x - y - z = 0
Then, the sum is equal to:
x + y + z = 10,000
9x - y - z = 0
10x - 0 - 0 = 10,000
10x = 10,000
x = 10,000/10
x = 1,000
Replacing x on the second equation, we get:
9x - y - z = 0
9*1,000 - y - z = 0
9,000 - y - z = 0
-y - z = - 9,000
Now, we can add the equation with the third one as:
-y - z = - 9,000
y - 5z = 0
0 - 6z = -9,000
-6z = -9000
z = -9000/(-6)
z = 1,500
Finally, using the third equation, the value of y is equal to:
y = 5z
y = 5*1500
y = 7,500
Therefore, you will invest 7,500 in stocks, 1,500 in bonds and you will leave 1,000 in savings.
in an election being held by the associated students organization, there are eight candidates for president, five for five president, five for secretary, and seven for treasurer. How many different possible outcomes are there for this election?
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we have
eight candidates for president
five for secretary
seven for treasurer
therefore
The different possible outcomes is giving by
(8)*(5)*(7)=280 outcomes
the answer is 280 outcomes24. Which point is part of the solution for the system of inequalities graphed below? A. (-1,-2) B. (3,1) C. (1,-2) D. (-3,1)
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The solution must be insige the red grind so we can see that the only point inside this area is the coordinate (-3, 1) so the answer is D
what is the pi of 53/17
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One way to calculate pi is by dividing the circunferemce by the diameter. So you just need to calculate the ratio 53/17. Using a calculator you get that
[tex]\frac{53}{17}=3.11764[/tex]36 unless for feeling nice to answer the 3 of them
Answers
36.
y=3x+2
f(x) can replace y
the answer is y
Find the slope-intercept form of the line that satisfies the given conditions.x-intercept 8, y-intercept −3
Answers
Given:
A line satisfies the given conditions.
x-intercept 8, y-intercept −3
The x-intercept is the value of x when y = 0
The y-intercept is the value of y when x = 0
So, the given line passes through the points (8, 0) and (0, -3)
We will find the slope using the following formula:
[tex]$$slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]Substitute with points:
[tex]m=\frac{-3-0}{0-8}=\frac{-3}{-8}=\frac{3}{8}[/tex]The slope-intercept form is: y = m * x + b
substitute m = 3/8 and b = -3
So, the answer will be, that the equation of the line is as follows:
[tex]y=\frac{3}{8}x-3[/tex]What is the shape of the base of each prism? (The base is not alwaysthe bottom)?A=B=C=D =E=F=
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A)
The base of the figure A is;
Here the base is in the shape of triangle.
A) Triangle
B)
how do i find the volume to the nearest 1 decimal place?
Answers
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} V=\pi\times r^2\times h \\ where \\ V\Rightarrow volume\text{ of the cylinder} \\ r\Rightarrow radius\text{ of its circular ends} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylinder below:
we have
[tex]\begin{gathered} height\text{ of the cylinder = 4 cm} \\ diameter\text{ of the circular end = 2 cm} \end{gathered}[/tex]but
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \Rightarrow r=\frac{d}{2}=\frac{2cm}{2}=1\text{ cm} \end{gathered}[/tex]Thus, the volume of the cylinder is evaluated by substituting the values of 4 cm and 1 cm for h and r respectively into the volume formula.
[tex]\begin{gathered} V=\pi\times1cm\times1cm\times4cm \\ =12.56637 \\ \approx12.6\text{ cubic centimeters} \end{gathered}[/tex]Hence, the volume of the cylinder, to the nearest 1 decimal place is
[tex]12.6\text{ cubic centimeters}[/tex]A caterer uses 4 pans of lasagna to serve 30 people. At this rate, how many pans of lasagna does the caterer use to serve 390 people?
A. 13
B. 52
C. 90
D. 98
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What formula do I use to get my answer? I’m getting 1/13, but my answer is incorrect. Thank you.
Answers
We will have the following:
First, the probability of getting the first t-shirt white will be:
[tex]p_1=\frac{4}{9}[/tex]And the probability of getting the second t-shirt white will be:
[tex]p_2=\frac{3}{8}[/tex]Now, the probability of getting the two white t-shirts one after the other will be:
[tex]\begin{gathered} p_3=p_1\ast p_2\Rightarrow p_3=\frac{4}{9}\ast\frac{3}{8} \\ \\ \Rightarrow p_3=\frac{1}{6} \end{gathered}[/tex]So, the probability of getting the two white t-shirts one after the other is 1/6.
What is the volume of the following prism?this is a prism with a right triangle as the base. The width of the triangle is 8 inches and the height of the triangle is 8 inches. The height of the prism is 12 inches.A. 768 m³B. 150 m³C. 384 m³D. 374 m³
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Given the following information
Volume of the prism=?
base of the prism= right triangle
volume of a prism with a right triangle as a base is given by
[tex]\frac{1}{2}*b*a*h[/tex]where
b= base of the triangle = 8
a= height of the triangle = 8
h= height of the prism=12
[tex]V=\frac{1}{2}8*8*12[/tex][tex]V=\frac{768}{2}[/tex][tex]V=384m^3[/tex]if ZQPS is a right angle and mLQPR = 71 ° . what is mZRPS
Answers
Step 1:
A right angle is 90 degree
Step 2:
angle
angle
angle
Step 3:
Sum of angle QPR and RPS = 90 i.e right angle
angle RPS = 90 - 71
m
Josh bought a new scooter for $412. He plans to make equal payment of $42 each month until the scooter is paid in full. About how many payments will Josh make? 10 20 5 or 15
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Data:
T=Total price of the scooter: $412
M=Every month he pays: $42
t= number of payments
[tex]t=\frac{T}{M}[/tex][tex]t=\frac{412}{42}=9.8\approx10[/tex]can someone help me i wikll give 25 pints but i need it now PLS
Answers
Answer:
Its in the picture below
(5x^5-y)^2 binomials to power
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Answer:
The expansion of the expression gives;
[tex]=25x^{10}-10x^5y+y^2[/tex]Expansion:
Given the expression:
[tex](5x^5-y)^2[/tex]We want to expand;
[tex]\begin{gathered} (5x^5-y)^2 \\ =(5x^5-y)(5x^5-y) \\ =5x^5(5x^5-y)-y(5x^5-y) \\ =5x^5(5x^5)+5x^5(-y)-y(5x^5)-y(-y) \\ =25x^{10}-5x^5y-5x^5y+y^2 \\ =25x^{10}-10x^5y+y^2 \end{gathered}[/tex]Therefore, the expansion of the expression gives;
[tex]=25x^{10}-10x^5y+y^2[/tex]19. If the cost price of 18 apples is the same as selling price of 16 apples, what is the profit in $ as well as percentage gain?
Answers
Answer
Percent Gain = 12.5%
Explanation
We are told that the
cost price of 18 apples = selling price of 16 apples
Let the cost price of an apple be x dollars
Let the selling price of an apple be y dollars
Buying 18 apples will cost 18 × x = (18x) dollars
Selling 16 apples will bring in 16 × y = (16y) dollars
Recall,
cost price of 18 apples = selling price of 16 apples
18x = 16y
We can rewrite as
16y = 18x
Divide both sides by 16
(16y/16) = (18x/16)
y = 1.125x
Percent gain is calculated as
[tex]\text{Percent Gain = }\frac{(\text{Selling price)-(Cost price)}}{Cost\text{ price}}\times100\text{ percent}[/tex]Selling price = y
Cost price = x
But recall that
y = 1.125x
[tex]\begin{gathered} \text{Percent Gain = }\frac{y-x}{x}\times100\text{ percent} \\ =\frac{1.125x-x}{x}\times100\text{ percent} \\ =\frac{0.125x}{x}\times100\text{ percent} \\ =0.125\times100\text{ percent} \\ =12.5\text{ percent} \end{gathered}[/tex]Hope this Helps!!!
Convert: 9 kilogramsmilligrams
Answers
Answer
9,000,000 milligrams
Step-by-step explanation
1 kilogram is equivalent to 1,000,000 milligrams. Using this conversion factor, the equivalence of 9 kilograms is found as follows:
[tex]\begin{gathered} 9\text{ kg }=9\text{ kg}{}\cdot\frac{1,000,000\text{ mg}}{1\text{ kg}} \\ \text{ SImplifying the units:} \\ 9\text{ kg }=9\cdot1,000,000\text{ mg} \\ 9\text{ kg}=9,000,000\text{ mg} \end{gathered}[/tex]What is the solution to the inequality below?1x1 < 5A. x < 5 or x>-5B. x>5 and x < -5C. x < 5 and x > -5D. x > 5 or x<-5
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The Solution is given by:
[tex]\lvert x\rvert<5[/tex]This means that:
[tex]-5So it follows that:[tex]x<5\text{ and x>-5}[/tex]Hence option C is correct.
You roll a six-sided dice.Event A: Roll a 6. Event B: Roll a prime number. Find P(A or B) . Express your answer as a fraction in simplest form.
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The probability of rolling a 6 is:
[tex]P(A)=\frac{1}{6}[/tex]There are 3 prime numbers between 1 and 6: 2, 3 and 5. Therefore, the probability of rolling a prime number is:
[tex]P(B)=\frac{1}{3}[/tex]Therefore, the probability of rolling a 6 or a prime number is:
[tex]P(AorB)=\frac{1}{6}+\frac{1}{3}=\frac{1}{2}[/tex]my name is Emma I'm 9 years old I'm in third grade
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From the question we can deduce that, the squares shaded in red represent the area tomatoes are planted in the garden.
The squares unshaded represents the area corn is planted in the garden.
Observe carefully that the total squares shaded in red are 24 (that is 4 by 6 OR 4 times 6). The unshaded squares total 18 (that is 3 times 6).
Each unit (or each square) is 1 square foot. This means on Nora's garden, she has tomatoes planted on 24 square feet. Also she has corn planted on 18 square feet.
Therefore, the difference between both areas is
Difference = 24 - 18
Difference = 6
ANSWER:
There are 6 more square feet of tomatoes than corn in Nora's garden.
The correct answer is option D
Rewrite the division problem into a multiplication problem 1/4 ÷ 3/5
Answers
ANSWER
[tex]\text{ }\frac{1}{4}\cdot\text{ }\frac{5}{3}[/tex]EXPLANATION
We want to rewrite the division problem into a multiplication one.
To do this, we have to change the division sign to a multiplication sign, and then, we invert the fraction on the right.
That is:
[tex]\begin{gathered} \frac{1}{4}\div\frac{3}{5} \\ \Rightarrow\text{ }\frac{1}{4}\cdot\text{ }\frac{5}{3} \end{gathered}[/tex]That is the answer.
Margaret and Nathan spent a total of $128 at the state fair last weekend. Nathan spent $2 more than twice the amount that Margaret spent. How much did Nathan spend at the fair?
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Let 'y' represent the amount Margaret spent at the state fair.
Let 'x' represent the amount Nathan spent at the state fair.
In the next statement, Nathan spent $2 more than twice the amount that Margaret spent.
Mathematically,
[tex]x=2+2y\ldots\ldots.1[/tex]And also, we were told that Margaret and Nathan spent a total of $128 at the state fair.
Mathematically,
[tex]x+y=\text{ \$128}\ldots\ldots\ldots2[/tex]Let us substitute 'x'= 2+2y into equation 2 and solve for y.
[tex]\begin{gathered} x+y=128 \\ 2+2y+y=128 \\ 2y+y=128-2 \\ 3y=126 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3y}{3}=\frac{126}{3} \\ y=42 \end{gathered}[/tex]Therefore, the amount of money spent by Nathan will be,
[tex]\begin{gathered} x=2+2y \\ x=2+2(42)=2+84=86 \\ \therefore x=86 \end{gathered}[/tex]Hence, Nathan spent $86 at the fair.
What percentage of the data values falls between the values pf 3 and 24 in the data set shown? 0 5 10 15 20 25 O 25% O 50% O 75% O 100%
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The graph shown in the image is a box and whiskers plot.
The sides of the box are determined by the first and third quartiles of the sample.
The left side corresponds to the first quartile (Q₁), this value separates the bottom 25% of the sample from the top 75%
The right side corresponds to the third quartile (Q₃), this value separates the bottom 75% of the sample from the top 25%
The line inside the box represents the second quartile (Q₂), this value is also known as the Median of the sample and divides the bottom 50% from the top 50%.
The body of the box, i.e. the space between Q₁ and Q₃, is the interquartile range (IQR), this represents the mid 50% of the sample.
The left whisker links the first quartile with the minimum value of the sample.
The right whisker links the third quartile with the maximum