The given equation is expressed as
3(x+1)=5-2(3x+4)
The first step is to open the brackets on each side of the equation by multiplying the terms inside the bracket by the terms outside the bracket. It becomes
3 * x + 3 * 1 = 5 - 2 * 3x + - 2 * 4
3x + 3 = 5 - 6x - 8
3x + 6x = 5 - 8 - 3
9x = - 6
x = - 6/9
x = - 2/3
A garage has 60 vehicles for sale, which
are all either new or second-hand.
28 of the vehicles are cars and the rest are
vans.
Of the cars, 7 are second-hand.
5 of the vans are new.
a) By copying and completing the
frequency tree below to show this
information, work out the value that should
replace D in the frequency tree.
b) In total, how many of the vehicles are
second-hand?
The number of vehicles that are secondhand is 34.
There is a garage. The total number of vehicles in the garage is 60. The vehicles are for sale. The vehicles are all either new or secondhand. The number of vehicles that are cars is 28. The other vehicles are vans. Seven of the cars are secondhand. Five of the vans are new. We have to find the total number of second-hand vehicles.
First of all, we will find the number of vans in the garage. The number of vans is 60 - 28 = 32. The number of cars that are second-hand is 7. The number of vans that are second-hand is 32 - 5 = 27.
The total number of second-hand vehicles in the garage is the sum of the numbers of second-hand cars and vans.
N = 7 + 27
N = 34
Hence, 34 vehicles are second-hand in the garage.
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12) Alyssa draws a rectangle that is 2/3 of ameter long and 3/5 of a meter wide. What isthe area of this rectangle?
A=LW
L=2/3
W=3/5
A= (2/3)(3/5)
A=2/5 or 0.4
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side a? Round your answer to the nearest whole number, if necessary.c = 9 cmA = 22°C = 13°Answers24 cm40 cm5 cm15 cm
Given
There is a triangle with sides a, b, and c and angles A, B, and C.
And,
c = 9 cm
A = 22°
C = 13°
To find:
The value of a.
Explanation:
It is given that,
There is a triangle with sides a, b, and c and angles A, B, and C.
And,
c = 9 cm
A = 22°
C = 13°
That implies,
By using sine law,
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \Rightarrow\frac{\sin13\degree}{9}=\frac{\sin22\degree}{a} \\ \Rightarrow a=\frac{9\times\sin22\degree}{\sin13\degree} \\ \Rightarrow a=14.9875 \\ \Rightarrow a=15cm \end{gathered}[/tex]Hence, the value of a is 15cm.
Hi I really do need help with this question. You don’t have to show work but it says we have to explain our answer.
The Solution:
Pattern A: start with 1 and add 3.
[tex]1,\text{ 4, 7, 10, 13}[/tex]Pattern B: Start with 1 and add 4.
[tex]1,\text{ 5, 9, 13, 17}[/tex]Comparing the two patterns, we have that:
Recall:
Median means the middle number.
The median of pattern A is 7 while that of pattern B is 9.
Thus, the median of pattern B is more than the median of pattern A by 2.
The scatter plot and line of best fit below show the length of 12 people's femur (thelong leg bone in the thigh) and their height in centimeters. Based on the line of besfit, what would be the predicted height for someone with a femur length of 72 cm?Answer: ____ cm.
Answer:
230
Explanation:
First, we find the equation fo the line point-slope form.
The slope of the line is
[tex]m=\frac{209-202}{63-60}=\frac{7}{3}[/tex]With the slope of the line in hand, we now write the point-slope form of the equation using the point (63, 209)
[tex]y-209=\frac{7}{3}(x-63)[/tex]With the equation of the line in hand, we now use it to find the value of y at x = 72.
Putting in x = 72 in the above equation gives
[tex]y-209=\frac{7}{3}(72-63)[/tex][tex]y-209=\frac{7}{3}\cdot9[/tex][tex]y-209=21[/tex]adding 209 to both sides gives
[tex]y=230[/tex]which is our answer!
Hence, the predicted height for someone with a femur length of 72 cm is 230 cm.
Is the LCD Going to be 5 • 7 •z = 35 ?
To add these fractions, we can do the following steps.
Step 1: Simplify each fraction.
[tex]\frac{25}{5y}=\frac{5\cdot5}{5y}=\frac{5}{y}[/tex][tex]\frac{64}{8y}=\frac{8\cdot8}{8y}=\frac{8}{y}[/tex]Step 2: We add the numerators since the fractions have the same denominator.
[tex]\frac{5}{y}+\frac{8}{y}=\frac{5+8}{y}=\frac{13}{y}[/tex]Therefore, the result of adding the fractions is 13/y.
6:4= :2 I dont know what that is
Answer: x = 3
Let the missing number be x
6 : 4 = x : 2
ratio is the same as fraction
6/4 = x/2
Step2 : cross multiply
x * 4 = 6 * 2
4x = 12
Divide both sides by 4
4x/4 = 12/4
x = 3
Therefore, the missing number is 3
When oil was spilled out in the middle of a lake, it spread out on the surface of the water in a circular pattern. The radius of the circular pattern increased at a rate of 4 feet per minute.((() = 4tft/min)Find the radius and area of the circular pattern of oil 5 minutes after the oil starts to spread.
The radius of the circle increases by 4 feet per minute. When 1 minute has passed, the radius is 4 feet, and when 5 minutes have passed, the radius will be 5 times that:
[tex]4\times5=20[/tex]The radius of the circle after 5 minutes is 20 feet.
To find the area, we use the formula for the area of a circle:
[tex]A=\pi r^2[/tex]Using the radius of 20 feet:
[tex]r=20ft[/tex]And substituting it into the formula for the area:
[tex]\begin{gathered} A=\pi(20ft)^2 \\ A=\pi(400ft^2) \end{gathered}[/tex]Using:
[tex]\pi=3.1416[/tex]We get the are of the circular pattern:
[tex]\begin{gathered} A=(3.1416)(400ft^2) \\ A=1,256.64ft^2 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} r=20ft \\ A=1,256.64ft^2 \end{gathered}[/tex]2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.
2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.
Let
x ------> the number of ounces of frozen yogurt
y ------> the total charge
we have the ordered pairs
(3.6,4.47) and (4.8,5.01)
step 1
Find the slope pr unit rate
m=(5.01-4.47)/(4.8-3.6)
m=$0.45 per ouncestep 2
Find the equation in point slope form
y-y1=m(x-x1)
we have
m=0.45
(x1,y1)=(3.6,4.47)
substitute
y-4.47=0.45(x-3.6)
convert to slope intercept form
y-4.47=0.45x-1.62
y=0.45x+2.85
In this problem, the y-intercept or initial value correspond to the charge for the cone
so
$2.85Which is the better buy? 36-fluid-ounce carton of apple juice for $8.28 6-cup carton of apple juice for $5.76
In this case, what we must do is calculate the price per unit each one:
[tex]\begin{gathered} 1\text{cup}=8ounce \\ \frac{8.28}{36}=0.23 \\ \frac{5.76}{6\cdot8}=0.12 \end{gathered}[/tex]therefore, the second purchase is better because it cost $0.12 per ounce, otheriwse the other purchase compares that they are $0.23 per ounce
Using the image below. Write the equation of the line fully simplified slope-intercept form. NO SPACES BETWEEN TERMS * just letting you know the answer is not y=-5x+2 or y=6x+2
The slope-intercept form is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]From the given graph, the line passes through points (1, -4) and (0, 2)
Let (x1, y1) = (1, -4) and (x2, y2) = (0, 2)
[tex]\begin{gathered} m=\frac{2-(-4)}{0-1} \\ m=\frac{2+4}{-1} \\ m=\frac{6}{-1} \\ m=-6 \end{gathered}[/tex]Substitute the value of m in the form of the equation
[tex]y=-6x+b[/tex]Since the line intersects the y-axis at point (0, 2)
Then the y-intercept is 2
Then b = 2
The equation of the line is
[tex]y=-6x+2[/tex]Write the function in factored form.
y = -2x³-4x²+4x+30x
I need help :)
The factored form is y = 2x(−x²−2x+17).
From the question, we have
y = -2x³-4x²+4x+30x
=−2x³−4x³+4x+30x
=−2x³−4x³+34x
=2x(−x²−2x+17)
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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find the length between the big circle and small circle.
First, we will calculate the hypotenuse of the first triangle
[tex]\begin{gathered} \cos 51=\frac{11}{h} \\ h=\frac{11}{\cos51} \\ h=17.48 \\ \end{gathered}[/tex]Now let's calculate the angle a
[tex]\begin{gathered} a=180-64-54 \\ a=65 \end{gathered}[/tex]Total result
T = 17.48+12.204+2.62+4.72
T = 37.024
The answer would be 37.024
for all triangles input data entered: side a, b and angle γ.
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^2=a^2+b^2-2ab\cos \gamma[/tex]Writing an equation of an… Given the foci and major axis length
We need to find the equation of the ellipse given the foci and major axis.
The equation is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]We have the foci points at (2,4) and (2,-6). The distance is 10 units, then the center is equal to half value c=5.
If the length of the major axis is 12.
Major axis length = 2a
Then
12 = 2a
a=12/2
a=6
To find b, we have the next equation:
[tex]\begin{gathered} b^2=a^2-c^2 \\ Replacing \\ b^2=6^2-5^2 \\ b^2=36-25 \\ b^2=11 \\ Solve\text{ for b} \\ b=\sqrt[]{11} \end{gathered}[/tex]Now, the center c is given by the point (2,-1). This point is in the middle of both foci points
Finally, we can replace on the ellipse equation:
[tex]\begin{gathered} \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1 \\ Replacing,\text{ the result is} \\ \frac{(x-2)^2}{6^2}+\frac{(y-(-1))^2}{(\sqrt[]{11})^2}=1 \end{gathered}[/tex]Question Solve: s + 159 = 25.
We have to solve for s:
[tex]\begin{gathered} s+159=25 \\ s+159-159=25-159 \\ s=-134 \end{gathered}[/tex]Answer: s = -134
a rectangle is drawn so the width is 71 inches longer than the height if the rectangles diagonal measurement is 85 inches find the heightround to 1 decimal place______inches
Let's first conceptualize the given details by drawing a rectangle with the given details being reflected.
Where,
x = Height of the rectangle
x + 71 = The ratio of the width of the rectangle with respect to the height.
Cutting the rectangle in half along the diagonal line makes a right triangle,
Thus, we can use the Pythagorean Theorem to be able to determine the height of the rectangle. We get,
[tex]\text{ a}^2+b^2=c^2\text{ }\rightarrow(x+71)^2+(x)^2=(81)^2_{}[/tex][tex]\text{ x}^2+142x+5041+x^2\text{ = 6561}[/tex][tex]\text{ 2x}^2\text{ + 142x + 5041 - 6561 = 0}[/tex][tex](\frac{1}{2})\text{ (2x}^2\text{ + 142x - }1520)\text{ = 0}[/tex][tex]\text{ x}^2\text{ + 71x - 760 = 0}[/tex][tex]\text{ (x +}\frac{71+\sqrt[]{8081}}{2})(x\text{ + }\frac{71\text{ - }\sqrt[]{8081}}{2})=\text{ 0}[/tex]There are two possible height of the rectangle,
[tex]x_1\text{ = }\frac{-71-\sqrt[]{8081}}{2}\text{ = -80.45 in.}[/tex][tex]\text{ x}_2\text{ = }\frac{-71\text{ + }\sqrt[]{8081}}{2\text{ }}=9.45\text{ in.}[/tex]9.45 = 9.5 in. is the most probable height of the rectangle because a dimension must never be negative, thus, let's adopt 9.5 in. as the height.
The width must be = x + 71 = 9.5 + 71 = 80.5 in.
Find the range of the function.f(x) = (x + 5)^2 + 8possible ans: y > - 8y ≥ 8y > 8All real numbers
SOLUTION
Given:
Explanation:
The range is the set of possible output values, which are shown on the y -axis.
The graph of the function will help us to find range.
Looking at the graph, the y values are from 8 up to infinity.
Final answer:
i only need help with question 3 thats in the attachment
Answer:
Step-by-step explanation:
3) Parallel and equal
b/c the sides are parallel, and also, b/c there is a right angle in the interior, it makes the sides equal length also.
The probability that it is Tuesday and Robert is absent is 0.04.There are 5 school working days in a week and the probabilitythat it is Tuesday is 0.5. What is the probability that Robert isabsent given that today is Tuesday?
The probability is 8%.
From the question, we have
The probability that it is Tuesday and Robert is absent is 0.04.
P(Tuesday and absent) = 0.04
P(Tuesday) =0.5
P(absent/Tuesday) =0.04/0.5 = 0.08
=0.08*100%
=8%
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Two investments are made summing up to 8,800. For a certain year, theseinvestments yield P1,326 in simple interest. Part of the investment is allotted for14% and part for 16%. Find the amount invested at each rate
Given:
a.) Two investments are made summing up to 8,800.
b.) For a certain year, these investments yield P1,326 in simple interest.
c.) Part of the investment is allotted for 14% and part for 16%.
Recall: The simple interest formula.
[tex]\text{ I = Prt}[/tex]Where,
I = interest
P = principal amount
r = interest rate
t = time (in year)
Step 1:
P = 8,800
But it's been made into two investments.
Let,
A = investment 1
B = investment 2
We get,
A + B = 8,800 = P (Equation 1)
Step 2:
Part of the investment is allotted for 14% and part for 16%.
Thus,
For investment 1:
Ia = Art = A(14/100)(1) = 0.14A
For investment 2:
Ib = Brt = B(16/100)(1) = 0.16B
We get,
0.14A + 0.16B = 1,326 (Equation 2)
Step 3:
Substitute Equation 1 to Equation 2.
A + B = 8,800
A = 8,800 - B
0.14A + 0.16B = 1,326
0.14(8,800 - B) + 0.16B = 1,326
1,232 - 0.14B + 0.16B = 1,326
0.02B = 1,326 - 1,232
0.02B = 94
0.02B/0.02 = 94/0.02
B = 4,700
Let's now find A.
A + B = 8,800
A + 4,700 = 8,800
A = 8,800 - 4,700
A = 4,100
In Summary:
The amount invested at 14% is 4,100
The amount invested at 16% is 4,700
Suppose that tan(x)csc(x)=1/f(x).Write f(x) in terms of sin(x) and cos(x).f(x)=
Trigonometry
We are given the equation:
[tex]\tan (x)\csc (x)=\frac{1}{f(x)}[/tex]It's required to write f(x) in terms of the sine and cosine functions.
Taking the reciprocal of both sides of the equation:
[tex]f(x)=\frac{1}{\tan (x)\csc (x)}[/tex]Recall:
[tex]\begin{gathered} \tan (x)=\frac{\sin (x)}{\cos (x)} \\ \text{csc(x)}=\frac{1}{\sin (x)} \end{gathered}[/tex]Substituting:
[tex]f(x)=\frac{1}{\frac{\sin(x)}{\cos(x)}\frac{1}{\sin (x)}}[/tex]Simplifying:
[tex]f(x)=\frac{1}{\frac{1}{\cos(x)}}=\cos (x)[/tex]Thus:
f(x)= cos(x)
Counting in bases less than ten
Answer:
Step-by-step explanation:
84649347
convert 15.7cm of the circumference to inches
Answer: We have to convert 15.7cm into inches, the steps for the conversion are as follows:
[tex]\begin{gathered} 1in=2.54cm\rightarrow\frac{1\imaginaryI n}{2.54cm}=1 \\ \\ \frac{15.7cm}{1}\times\frac{1in}{2.54cm}=\frac{15.7}{2.54}in \\ \\ =6.18in \end{gathered}[/tex]Therefore the answer is 6.18in.
Which of the following equations are equivalent (i.e. have the same solution for x)? Check all that apply.A X+1=4B 9+X=6C -5+x=-2D 2+x=5E X+(-4)=7
Solve the following equations and find those that have the same solution for x.
A
x + 1 = 4
Subtracting 1:
x = 3
B
9 + x = 6
Subtracting 9:
x = -3
C
-5 + x = -2
Adding 5:
x = 3
D
2 + x = 5
Subtracting 2:
x = 3
E
x + (-4) = 7
Operating:
x - 4 = 7
Adding 4:
x = 11
Only equations A, C, and D are equivalent
Find the area of this irregular shape.
[Round off to the nearest whole number.]
sq. units
Answer:
grubby me and I will be there in a few minutes to talk to you about it do you
nose
Step-by-step explanation:
nosediving the Gigi Hadid and wirt me and wirt me and I will be there in a few minutes to talk to you about it
Graph f(x)=log1/2 (x)
The coordinate are (0.8,0)
Answer:
Step-by-step explanation:
Which should figure could be formed from the net shown?
Answer
The solid figure that could be formed from the net show is a square pyramid
Explanation
The figure shown has been opened from the vertex, v, when closed, a square base of side 5 in with perpendicular height 7 in is formed. Hence, the solid figure that could be formed from the net shown is a Square pyramid
Re-write the equation in slope-intercept form: 3x - 2y =6
To write it in the slope intercept form we have to slove the equation to y:
[tex]\begin{gathered} 3x-2y=6\rightarrow \\ 2y=3x-6 \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]What is the volume of the prism shown by the net?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
length = 1/2 yd
width = 1/4 yd
height = 1/6 yd
Volume = ?
Step 02:
Volume = l * w * h
[tex]V\text{ = }\frac{1}{2}yd\cdot\frac{1}{4}yd\cdot\frac{1}{6}yd=\frac{1}{48}yd^3[/tex]The answer is:
The volume of the right rectangular prism is 1 / 48 yd³ .
let f(x) = 10x-10. Find the value of (f o f^-1) (-10)a)0b)1c)10d)-10
Solution
We are given the following expression to evaluate:
[tex]\begin{gathered} f(x)=10x-10 \\ \\ \text{ Find:} \\ (f\mathrm{}f^{-1})(-10) \end{gathered}[/tex]- In order to solve this question, we should apply the following theorem:
[tex]f(f^{-1})(x)=x_{}[/tex]- Thus, in order to solve the question, we simply substitute x = -10. This is done below:
[tex]\begin{gathered} f(f^{-1})(x)=x \\ \text{put }x=-10 \\ \\ f(f^{-1})(-10)=-10\text{ (OPTION D)} \end{gathered}[/tex]Final Answer
The answer is:
[tex]f(f^{-1})(-10)=-10\text{ (OPTION D)}[/tex]