Explanation
Step 1
[tex]\begin{gathered} a+15=32 \\ \text{subtract 15 in both sides} \\ a+15-15=32-15 \\ a=17 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} b-12=75 \\ \text{add 12 in both sides} \\ b-12+12=75+12 \\ b=87 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} 9x=90 \\ we\text{ n}eed\text{ isolate x, so divide both sides by 9} \\ \frac{9x}{9}=\frac{90}{9} \\ x=10 \end{gathered}[/tex]Step 4
[tex]\begin{gathered} \frac{x}{6}=7 \\ \text{Multiply both sides by 6} \\ \frac{x}{6}\cdot6=7\cdot6 \\ x=42 \end{gathered}[/tex]I hope this helps you
What is the solution of 5|2x + 1| – 3 ≤ 7?
Given
5|2x + 1| – 3 ≤ 7
Find
Solve the inequality
Explanation
[tex]\begin{gathered} 5|2x+1|-3\leq7 \\ 5|2x+1|\leq7+3 \\ 5\lvert2x+1\rvert\leq10 \\ |2x+1|\leq\frac{10}{5} \\ \\ |2x+1|\leq2 \end{gathered}[/tex]we know that
[tex]2x+1\leq2\text{ }and\text{ }2x+1>-2[/tex]so ,
[tex]\begin{gathered} 2x+1\leq2 \\ 2x\leq1 \\ x\leq\frac{1}{2} \\ \\ and \\ \\ 2x+1\ge-2 \\ 2x\ge-2-1 \\ 2x\ge-3 \\ x\ge-\frac{3}{2} \end{gathered}[/tex]so ,
[tex]-\frac{3}{2}\leq x\leq\frac{1}{2}[/tex]Final Answer
Hence , the correct option is
[tex]-\frac{3}{2}\leq x\leq\frac{1}{2}[/tex]$3,700 for 2% for 4 yearswhat is the simple interest?what is the total amount?
Here, we want to get the amount on the simple interest
Mathematically, this is the sum of the amount deposited and the interest accurred
For the interest, we use the formula for simple interest as follows;
[tex]\begin{gathered} I\text{ = }\frac{PRT}{100} \\ \\ P\text{ is the amount deposited = \$3,700} \\ R\text{ is the rate which is 2\%} \\ T\text{ is time which is 4 years} \\ \text{Substituting these values;} \\ I\text{ = }\frac{3700\times2\times4}{100}\text{ = \$296} \end{gathered}[/tex]So, we simply add this to the principal to get the amount
[tex]\begin{gathered} \text{Amount = Principal + Interest} \\ =\text{ \$3,700 + \$296 = \$3,996} \end{gathered}[/tex]Given R(I, y) = (-y, z) and the point Qt1, 0), what is R(Q)?R(Q)
Given that R(x, y) = (-y, x)
This is a transformation.
We want to find R(Q)
The point Q is given as:
Q = (1, 0)
This means that x = 1 and y = 0
Therefore, for R(Q):
-y = -0 = 0
x = 1
Therefore:
R(Q) = (-y, x) = (0, 1)
1 Lola collects blood donations at a clinic. 7/16 of the donations are of Type 0, 3/8 are of Type A, and 1/16 are Type AB. The remaining are Type B. What part of the blood donations are Type B?
Answer:
n=1/8
Explanation:
From the diagram, if we sum up all the parts, we have:
[tex]\frac{7}{16}+\frac{3}{8}+\frac{1}{16}+n=1[/tex]We solve the equation above for n.
The lowest common multiple of 16 and 8 = 16
Therefore:
[tex]\frac{7+6+1}{16}+n=1[/tex]Therefore:
[tex]\begin{gathered} \frac{14}{16}+n=1 \\ n=1-\frac{14}{16} \\ n=\frac{16-14}{16} \\ n=\frac{2}{16} \\ n=\frac{1}{8} \end{gathered}[/tex]The value of n is 1/8.
For the following set of data, find the number of data within 1 population standarddeviation of the mean.68, 68, 70, 61, 67, 71, 63, 67
Given the following set of numbers,
[tex]68,\text{ 68, 70, 61, 67, 71, 63, 67}[/tex]Where the (n) number of data is 8, the mean is,
[tex]\bar{x}=\frac{x_1+x_2+..._{}+x_n}{n}=\frac{68+68+70+61+67+71+63+67}{8}=66.875[/tex]The standard deviation is 3.36
Hence, the interval that is 1 population within the mean is given by
[tex](66.88-3.36,66.88+3.36)=(63.52,70.24)[/tex]Of all the data only 71, 61, and 63 are not an element of the interval (63.52,70.24)
The total number of data is 8.
Hence, the total number of data within 1 standard deviation of the mean is 5
Find the missing sides of the triangle. Leave youranswers as simplified radicals.
Consider the following right triangle:
To find the missing sides x and y, we can apply the following trigonometric ratios:
[tex]\cos(60^{\circ})=\frac{adjacent\text{ side to the angle 60}^{\circ}}{Hypotenuse}[/tex][tex]\sin(60^{\circ})=\frac{opposite\text{ side to the angle 60}^{\circ}}{Hypotenuse}[/tex]and
[tex]\tan(60^{\circ})=\frac{opposite\text{ side to the angle 60}^{\circ}}{adjacent\text{ side to the angle 60}^{\circ}}[/tex]thus, applying the data of the problem to the last equation, we get:
[tex]\tan(60^{\circ})=\frac{opposite\text{ side to the angle 60}^{\circ}}{adjacent\text{ side to the angle 60}^{\circ}}=\frac{15}{y}[/tex]that is:
[tex]\tan(60^{\circ})=\frac{15}{y}[/tex]solving for y, we obtain:
[tex]y=\frac{15}{\tan(60^{\circ})}=\frac{15}{\sqrt{3}}[/tex]On the other hand, applying the above data to the first equation, we get:
[tex]\cos(60^{\circ})=\frac{adjacent\text{ side to the angle 60}^{\circ}}{Hypotenuse}=\frac{y}{x}=\frac{15}{\sqrt{3}}\text{ }\cdot\frac{1}{x}[/tex]or
[tex]\cos(60^{\circ})=\frac{15}{\sqrt{3}\text{ x}}\text{ }[/tex]solving for x, we obtain:
[tex]x=\frac{15}{\sqrt{3}\cdot\cos(60)}=\text{ }\frac{15}{\sqrt{3\text{ }}\cdot1/2}=\frac{2(15)}{\sqrt{3}}=\frac{30}{\sqrt{3}}[/tex]we can conclude that the correct answer is:
Answer:[tex]x=\frac{30}{\sqrt{3}}[/tex]and
[tex]y=\frac{15}{\sqrt{3}}[/tex]The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
The system of equation that represents lines F and G is (1) y = 1.75x + 3.5, y = -4x-8
To find the system of equation, we will put the values given tables in the equation given in the options.
For option (1)
y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
Therefore, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
Learn more about system of equation on:
https://brainly.com/question/24065247
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Bob bought a $800 TV on sale for $650. What is the percent he saved?
Answer:
18.75%
Step-by-step explanation:
Since you want to know what percent he saved, first you have to figure out how much he saved.
800 - 650 = 150
Then to find the percent, find how much 150 is of 800.
[tex]\frac{150}{800} = 0.1875[/tex]
Since we're finding a percentage, multiply by a 100.
0.1875 × 100 = 18.75%
If it said to round, the answer would be 19%, but it doesn't, so keep it at 18.75%.
In ∆QRS, q =370 cm, r =910 cm and
using cosine rule
[tex]\begin{gathered} s^2=r^2+q^2-2rq\cos S \\ s^2=910^2+370^2-2\times910\times370\cos 31 \\ s^2=828100+136900-336700\times0.8571673007 \\ s^2=965000-288608.230146 \\ s^2=676391.769854 \\ s=\sqrt[]{676391.769854} \\ s=822.430404262 \\ s=822\operatorname{cm} \end{gathered}[/tex]The two shorter sides of a right triangle measure 18 ft and 24 ft. What is the measure in feet of the third side?
We have that in a right triangle, the larger side is the hypothenuse since the sum of the others angles must be equal to 90. Thus, we can apply the Pythagorean Theorem to solve this question.
The legs of the triangle are a = 18 ft, b = 24 ft, and c = ?.
Then, applying the Pythagorean Theorem, we have (without using units):
[tex]c^2=a^2+b^2\Rightarrow c^2=(18)^2+(24)^2\Rightarrow c^2=324+576\Rightarrow c^2=900[/tex]Then, taking the square root to both sides of the equation, we have:
[tex]\sqrt[]{c^2}=\sqrt[]{900}\Rightarrow c=30[/tex]Then, the measure of the third side (hypothenuse) is c = 30 ft.
describe the domain of the function f(x;y)= ln(4-x-y)
Domain of the given function is x∈(-2,∞)
Step-by-step explanation:
The given function is y=\ln(x+2)y=ln(x+2)
Domain is the set of x values for which the function is defined.
And we know that logarithm function is defined only for values greater than zero.
Therefore, for domain we have
x + 2 >0
x > -2
Hence, the domain of the
The domain of the function
f
(
x
,
y
)
=
ln
(
4
−
x
−
y
)
is the region of the x-y plane such that the argument of logarithm function is positive,...
See full answer below.
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What Is Domain and Range in a Function?
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Chapter 7 / Lesson 3
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What are the domain and range of a function? What are the domain and range of the graph of a function? In this lesson, learn the definition of domain and range as it applies to functions as well as how it applies to graphs of functions. Moreover, there will be several examples presented of domain and range and how to find them.
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5. The function w(x) = 70x represents the number of words w(x) you can type in x minutes. SHOW ALL WORK!!a.) How many words can you type in 5 minutes?b.) How many words can you type in 8 minutes?c.) How long would it take to read 280 words?
The given function is
[tex]w(x)=70x[/tex]Where x is minutes.
(a) To find the number of words typed in 5 minutes, we just need to replace the variable for 5 and solve
[tex]w(5)=70(5)=350[/tex]Therefore, there are typed 350 words in 5 minutes.
(b) We do the same process for 8 minutes.
[tex]w(8)=70(8)=560[/tex]Therefore, there are typed 560 words in 8 minutes.
(c) To find the type for 280 words, now we replace the other variable w(x), and solve for x
[tex]280=70x[/tex]We divide the equation by 70
[tex]\frac{280}{70}=\frac{70x}{70}\rightarrow x=4[/tex]Therefore, 280 words take 4 minutes.
the sum of 5 times a number and twice its cube
Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 4^-x=2.6What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set { } (simplify your answer. type an exact answer)B. There is no solution
Given:
[tex]4^{-x}=2.6[/tex]To solve for x:
Taking log on both sides
[tex]\begin{gathered} \log 4^{-x}=\log 2.6 \\ -x\log 4=\log 2.6 \\ -x=\frac{\log 2.6}{\log 4} \\ -x=0.689255811 \\ x=-0.689255811 \\ x\approx-0.689 \end{gathered}[/tex]Hence, the value of x is -0.689 (rounded to three decimal places).
Ivan took out a loan for 6700 that charges an annual rate of 9.5% compounded quarterly. Answer each part.
We will have the following:
a) The amount after one year will be:
[tex]\begin{gathered} A=6700(1+\frac{0.095}{4})^{4\ast1}\Rightarrow A=7359.53647... \\ \\ \Rightarrow A\approx7359.54 \end{gathered}[/tex]So, the amount after 1 year will be approximately $7359.54.
b) The effective annual interest rate will be:
[tex]eair=(1+\frac{0.095}{4})^4-1\Rightarrow eair=0.0984382791...[/tex]So, the effective annual interest rate will be approximately 9.84%.
А.
U. 3y2 +y-1
X-8
0.X-8+
G. X-3
+2x+1
D. 2k2+8k+15+
24
1. 3k +16 +-14
R X-1
Y. x2-3x +4 +
E. X+4
M. x2-8x +24 +-68
X+3
T. y2 – 8y +12
1 2 3
4 5
6 7
9
10
11
12
13 14
SOLUTION
After solving the numbers in front of the letters, we have:
A=4 ,B=14, C=2, D=6, E=1, F=15, G=17, H=27, I=33, J=3, K=40,L=22, M=5
N=19, O=11, P=16, Q=24, R=0, S=12, T=32, U=75, V=18, W=7, X=20, Y=35, Z=36
Now, we will match these numbers to the letters to form words.
4,16,0,33,22: APRIL
12,27,11,7,1,0,12: SHOWERS
5,4,35: MAY
15,22,11,7,1,0,12: FLOWERS
4,19,6: AND
1,18,1,0,35,32,27,33,19,17,12: EVERYTHING
33,19: IN
5 2/5 × 0.8A. 4.32B. 5.76C.7.80D.2.75
Answer:
A. 4.32
Explanation:
First, we need to transform the mixed number 5 2/5 into a decimal number as:
[tex]5\frac{2}{5}=5+\frac{2}{5}=5+0.4=5.4[/tex]Then, we can multiply 5.4 by 0.8, so:
[tex]5\frac{2}{5}\times0.8=5.4\times0.8=4.32[/tex]To multiply 5.4 by 0.8, we can multiply the numbers normally without taking into account the decimal points. So 54 times 08 is equal to:
Then, 5.4 has one digit after the decimal point and 0.8 has one digit after the decimal point. So, in total, we have two digits after the decimal point. It means that the result is equal to 4.32 because we need two digits after the decimal point.
Therefore, the answer is 4.32
Marisol wants to buy a backpack from the Gucci store. Gucci ishaving a sale of 45% off the regular price. If the regular price of aGucci backpack is $1375.23, then what will the new sale price beafter the discount of 45% is applied?
Regular price = $1375.23
Discount = 45% of Regular price
The discount = 45% of $1375.23
= 45/100 x $1375.23
= 0.45 x $1375.23
Discount = $ 618.85
But Sale price = Regular price - Discount
Sale price = $1375.23 - $618.85
Sale price = $756.38
Hence, the new sale price after the discount of 45% is applied is $756.38
Jeremiah can drink 64 fluid ounces of coffee in 4 days. How many Quarts of coffee can he drink in 1 hour.help explain please:)
1 quart = 32 fluid ounces
Therefore, 64 fluid ounces = 2 quarts
Jeremiah can drink these 2 quarts in 4 days meaning he drinks
[tex]2\frac{\text{quarts}}{4\text{days }}=0.5\frac{\text{quarts}}{\text{days}}[/tex]Now, there are 24 hours in a day; therefore, the number of quarts Jeremiah drinks in 1 hour is
[tex]\frac{0.5\text{quarts}}{24\text{hours}}=\frac{1}{48}\frac{\text{quarts}}{\text{days}}[/tex]or in decimal form, this is 0.021 quarts in an hour.
The points (−5, -5) and (r, 1) lie on a line with slope 1/2. Find the missing coordinate r.
Solution:
The slope is expressed as
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ where \\ (x_1,y_1)\text{ and} \\ (x_2,y_2)\text{ are the coordinates of points through which the line passes} \end{gathered}[/tex]Given that the points (-5, -5) and (r, 1) lie on the line with slope 1/2, this implies that
[tex]\begin{gathered} x_1=-5 \\ y_1=-5 \\ x_2=r \\ y_2=1 \end{gathered}[/tex]By substituting these valus into the slope formula, we have
[tex]\begin{gathered} \frac{1}{2}=\frac{1-(-5)}{r-(-5)} \\ \Rightarrow\frac{1}{2}=\frac{1+5}{r+5} \\ cross-multiply, \\ r+5=2(1+5) \\ \Rightarrow r+5=12 \\ add\text{ -5 to both sides of the equation,} \\ r+5-5=12-5 \\ \Rightarrow r=7 \end{gathered}[/tex]Hence, the missing coordinate r is evaluated to be
[tex]7[/tex]The scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 25 students.Use the equation of the line of best fit, =y+1.82x11.36, to answer the questions below.Give exact answers, not rounded approximations. (a) For an increase of one hour in time worked, what is the predicted increase in the amount of money spent on entertainment?$(b) What is the predicted amount of money spent on entertainment for a student who doesn't work any hours?$(c) What is the predicted amount of money spent on entertainment for a student who works 8 hours?$
Solution:
Given the scatterplot below:
where the equation of the line of best fit is expressed as
[tex]y=1.82x+11.36[/tex]A) Predicted increase in the amount of money spent on entertainment, for an increase of one hour in time worked.
Recall that the line equation is expressed as
[tex]\begin{gathered} y=mx+c \\ where \\ m=slope \\ slope=\frac{increase\text{ in y}}{increase\text{ in x}} \end{gathered}[/tex]By comparison with the equation of line of best fit, we see that
[tex]\begin{gathered} slope=1.82 \\ where \\ slope=\frac{increase\text{ in amout of money spent}}{increase\text{ in the number of hours worked}} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} 1.82=\frac{increase\text{ in amount of money spent}}{1} \\ \Rightarrow predicted\text{ increase in amount of money spent on entertainment = \$1.82} \end{gathered}[/tex]B) Predicted amount of money spent on entertainment for a student with no number of hours worked
This implies that from the equation of the line of best fit, the value of x is zero.
By substitution, we have
[tex]\begin{gathered} y=1.82(0)+11.36 \\ =0+11.36 \\ \Rightarrow y=\$11.36 \end{gathered}[/tex]C) Predicted amount of money spent on entertainment for a student with8 hours of work.
Thus, we have the value of x to be 8 from the equation of the line of best fit.
By substitution, we have
[tex]\begin{gathered} y=1.82\left(8\right)+11.36 \\ =14.56+11.36 \\ \Rightarrow y=\$25.92 \end{gathered}[/tex]solve each equation for y=. Without graphing, classify each system as having one solution, no solution, or infinitely many solutions.
x+y=3
y=2x-3
Answer:
The answer would be y=3, and there is only one solution.
Step-by-step explanation:
In the first expression, x+y=3, we can rearrange it to get it in terms of x so we can substitute it for x in the second expression.
x+y=3
Subtract y from both sides: x=-y+3
Substitute x=-y+3 into the second expression: y=2(-y+3)+3
Distribute the 2: y=-2y+6+3
Simplify the right side: y=-2y+9
Add 2y to both sides: 3y=9
Divide by 3: y=3
Since there is a single y coordinate, that means that there is only one solution.
I don't understand this, can you hell me solve this please?
We will investigate the angle measures and the properties involved with a pair of parallel lines.
We are given two pairs of parallel lines, namely:
[tex]\begin{gathered} L\text{ }\mleft\Vert\text{ m }\mright? \\ a\text{ }\mleft\Vert\text{ b}\mright? \end{gathered}[/tex]The angle properties that are used in consequence of parallel lines are of the following:
[tex]\text{Alternate Angles , Complementary Angles , Supplementary Angles, Corresponding Angles}[/tex]Each of the above property describes a relationship between two angle measures. That is how two angles are related to one another in consequence of the parallel lines.
The angle measures are classified into two types as follows:
[tex]\begin{gathered} \text{Interior Angles} \\ \text{Exterior Angles} \end{gathered}[/tex]Can someone help me with this math problem I have like 20 more and I really need help
We can find the x-intercept when y=0 so replacing y for 0 we have
[tex]\begin{gathered} -5x+2(0)=10 \\ -5x=10 \\ x=\frac{10}{-5}=-2 \end{gathered}[/tex]The x-intercept is (-2,0).
Now we are going to replace x for 0 to find the y-intercept
[tex]\begin{gathered} -5(0)+2y=10 \\ 2y=10 \\ y=\frac{10}{2}=5 \end{gathered}[/tex]The y-intercept is (0,5).
For the graph of 4x -9y=12 we have that the x-intercept is (3,0) and the y-intercept is (0,-4/3)
I hope you can help me with this I can’t understand it and I’ve already had three tutors turn me down because they didn’t understand it
Given:
An angle whose supplement is 10 degrees more than twice its complement.
Required:
To write and solve the equation.
Explanation:
Let the angle be x degrees.
Supplement of this angle = 180 - x
Complement of this angle = 90 -x
Given that supplement is 10 degrees more than twice its complement.
So the equation becomes:
180- x =2(90 - x) + 10
Solve by multiplication.
180 - x = 180 - 2x +10
Solve by collectiong the like terms.
2x - x = 180 - 180 + 10
x = 10 degrees
Final Answer:
The value of the angle is 10 degrees.
If a || band e l f, what is the value of y?(x + 1)[(x-3°
y = x + 1 [ alternate exterior angles ]
You are given the circumference of the circle and the measure of the central angle ACB. Find the length of arc AB.circumference = 36 feet; m ZACB= 40"The length of arc AB isfeet
the length of arc ACB is 4 ft
Explanation
the length of an arc is given by:
[tex]l=\frac{\theta}{360\text{ \degree}}2\text{ }\pi r[/tex]where l is the length or the arc, theta is the angle in degrees, r is the radius
so
Step 1
find the radius of the circle
[tex]\begin{gathered} 2\text{ }\pi r=36 \\ \text{divide boths ides by 2}\pi \\ \frac{2\text{ }\pi r}{2\text{ }\pi}=\frac{36}{2\pi} \\ r=\frac{18}{\pi} \end{gathered}[/tex]Step 2
now, replace in the formula
Let
angle= 40 °
[tex]\begin{gathered} l=\frac{\theta}{360\text{ \degree}}2\text{ }\pi r \\ l=\frac{40}{360\text{ \degree}}2\text{ }\pi(\frac{18}{\pi}) \\ L=\frac{40}{360}\cdot36 \\ l=4\text{ } \end{gathered}[/tex]therefore, the length of arc ACB is 4 ft
I hope this helps you
Round 6,752 to the nearest ten and nearest hundred.
Given the number:
6752
i) Round to the nearest ten:
To round to nearest ten means to rou
Given cos = 0.9528, find .
Given:
[tex]\cos \theta=0.9528[/tex]To find the value of θ,
[tex]\begin{gathered} \cos \theta=0.9528 \\ \theta=\cos ^{-1}(0.9528) \\ \theta=17.6739^{\circ} \end{gathered}[/tex]Victoria spends the two spinners shown 500 times solve a percent equation to predict the number of times the sum is less than or equal to 3. Enter the correct answers in the boxes.
Given t spinners :
The first has the numbers : from 1 to 5
The second has the numbers : from 1 to 3
So, the sum is less than or equal to 3 can get if the two spinners give 1 or 2
So, the probability to get 1 or 2 from the first spinner = 2/5
And the probability to get 1 or 2 from the second spinner = 2/3
So, total probability = 2/5 * 2/3 = 4/15 = 26.66%
She spends the two spinners 500 times
So, the equation will be :
[tex]26.66\%\times500=x[/tex]Solve for x:
[tex]26.66\%\times500=133.3[/tex]So, the number of times = 133