By definition, the sum of the interior angles of a triangle is 180 degrees.
In this case, you have the triangle ABC shown in the picture. Since you know the measure of two angles (angle B and angle C), you can set up the following equation:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ m\angle A+100\degree+47\degree=180\degree \end{gathered}[/tex]Finally, you need to solve for the angle A in order to find its measure. You get that this is:
[tex]\begin{gathered} m\angle A+147\degree=180\degree \\ m\angle A=180\degree-147\degree \\ m\angle A=33\degree \end{gathered}[/tex]The answer is:
[tex]33\degree[/tex]Which of the following would result in the correct amount of sugar?
Given
The sugar needed is 2/3 cups.
The amount of sugar founded is 1/2 cups.
To find the estimation of the remaining sugar needed.
Explanation:
It is given that,
The needed sugar is 2/3 cups.
The sugar found is 1/2 cups.
Let x the estimated amount.
Then,
[tex]\begin{gathered} \frac{2}{3}=\frac{1}{2}+x \\ x=\frac{2}{3}-\frac{1}{2} \\ x=\frac{4-3}{6} \\ x=\frac{1}{6} \end{gathered}[/tex]Hence, the answer is 1/6.
There are 450 taxi drivers in the city. 32% of the drivers are above 35 years of age. How many drivers, d, are above 35 years of age?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
The number of drivers above 35 years of age is 144.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Number of taxi drivers = 450
Number of drivers above 35 years of age = 32%
The number of drivers above 35 years of age:
= 32% of 450
= (32 /100) x 450
= 144
Thus,
The number of drivers above 35 years of age is 144.
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what is the value of y? -5y+3=2(4y+12)
ANSWER:
-21/13
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]-5y+3=2\mleft(4y+12\mright)\: [/tex]We solve for y:
[tex]\begin{gathered} -5y+3=8y+24 \\ 8y+5y=3-24 \\ 13y=-21 \\ y=-\frac{21}{13} \end{gathered}[/tex]The value of y is -21/13
Estimate the product by rounding to the nearest hundred 712*763
In order to estimate the product by rounding to the nearest hundred,
first, we need to round the given factors to the required place value, in this case, hundred.
712 is rounded down to 700
763 is rounded up to 800
[tex]\begin{gathered} 712\Rightarrow700 \\ 763\Rightarrow800 \end{gathered}[/tex]Then, we multiply the rounded numbers
[tex]700\cdot800=560,000[/tex]the estimated product is 560,000
[tex]712\cdot763\approx560,000[/tex]Consider f(x) = –4x2 + 24x + 3. Determine whether the function has a maximum or minimum value. Then find the value of the maximum or minimum. 1) maximum; 32) minimum; 33) maximum; 394) minimum; 39
Given the function:
[tex]f(x)=-4x^2+24x+3[/tex]The leading coefficient of the function is negative
So, the function has a maximum value
the graph of the function will be as shown in the following figure:
As shown the maximum value of the function = 39
So, the answer will be option 3) maximum; 39
please help I've been trying to solve this for a long time
The given system of inequalities is expressed as
[tex]\begin{gathered} 24x\text{ + 8y }\ge\text{ 20} \\ 3x\text{ - 6y > 24} \end{gathered}[/tex]The first step is to change the inequality symbols to that of 'equal to" and plot the straight line graph for each equation.
For the first equation, the line on the graph would be solid because the symbol is "greater than or equal to"
For the second equation, the line would be broken because the inequality symbol does not have an "=" symbol
The graph is shown below
if point C is between points A and B, then AC+CB
ANSWER
= AB
EXPLANATION
This is very easy to understand with a diagram of the segment:
The sum of the segments AC and CB is the same as the whole segment AB.
I will show you the pic
Let:
[tex]\begin{gathered} 3x+4y=-2\text{ (1)} \\ 2x-4y=-8\text{ (2)} \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ 3x+2x+4y-4y=-10 \\ 5x=-10 \\ \text{divide both sides by 5:} \\ \frac{5x}{5}=-\frac{10}{5} \\ x=-2 \\ \text{ Replace x into (1)} \\ 3(-2)+4y=-2 \\ 4y=4 \\ \text{divide both sides by 4:} \\ \frac{4y}{4}=\frac{4}{4} \\ y=1 \end{gathered}[/tex]O GRAPHS AND FUNCTIONSWriting equations of lines parallel and perpendicular to a given.
The equation of lines parallel and perpendicular given is, y = 2x - 15
Write equations of lines parallel and perpendicularStandard slope-intercept notation for parallel or perpendicular lines is
y = mx + b. (where "m" stands for the slope, and "b" represents the y-intercept). The slope is the only factor that distinguishes linear equations for parallel and perpendicular lines.
In other words, the sum of the reciprocal slopes of perpendicular lines is negative, or -1.
x+2y = -1
2y = -1-x
y = -1-x /2
Slope = -1/2
The slope of the perpendicular line is = 2
y-y₁ = m(x-x₁)
y = mx + b
-5 = 2(5) + b
-5 = 10 + b
-5- 10 = b
-15 = b
y = mx+ b
-5 = 2(5) + b
-5 = 10 + b
-15 = b
y = mx + b
y = 2x - 15
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Complete the square by filling in the missing bland to form a perfect square trinomial.
Solution
- The solution steps are given below:
[tex]\begin{gathered} x^2-6x+--- \\ \text{ To complete the square, we add the square of the half of the coeefficient of }x \\ \text{ That is, we add} \\ (-\frac{6}{2})^2=9 \\ \\ \text{ Thus, the perfect square is:} \\ x^2-6x+9 \end{gathered}[/tex]Final Answer
The answer is
[tex]x^2-6x+9[/tex]Find the perimeter of the region. + 90° 2 in. + 6 in. 90° 90° 6 in.
The perimeter of the region = Perimeter of the square - 4 x Quarter of a circle
Perimeter of the square = 4 x Length = 4 x 10= 40 inches
[tex]\begin{gathered} \text{Perimeter of one quarter of a circle= }\frac{2\pi r}{4} \\ =\frac{2\times3.142\times2}{4}\text{ = 3.142 inches} \end{gathered}[/tex][tex]\begin{gathered} \text{Perimeter of the shaded region = 40 - 4(3.142) } \\ =40-12.568\text{ =27.432 inches} \end{gathered}[/tex]A used car dealer has the following information for two months of sales:Month 1: 239 cars soldMonth 2: 324 cars soldWhat is the percent of increase/decrease ? Round to the nearest percent.
Answer:
36%
Explanation:
The information for two months of sales is:
• Month 1: 239 cars sold
,• Month 2: 324 cars sold
We can classify the given information as:
• Initial: 239 cars sold
• Final: 324 cars sold
When the initial value is less than the final value, you have a percentage increase.
Therefore:
[tex]\begin{gathered} \text{Percentage Increase =}\frac{\text{Final Value -Initial Value}}{\text{Initial Value}}\times100 \\ =\frac{\text{3}24-239}{\text{2}39}\times100 \\ =\frac{85}{239}\times100 \\ =36\%\text{ (to the nearest percent)} \end{gathered}[/tex]The percentage increase is 36% to the nearest percent.
How many bacteria will there be?Round to the nearest whole number
You know that:
- She puts a population of 300 bacteria into a favorable growth medium at 8:00 A.M.
- At 5:00 P.M. the population is 1100 bacteria,
- The next morning, at 8:00 A.M. she comes back to the lab.
By definition, an Exponential Growth Model has the following form:
[tex]P=P_0e^{rt}[/tex]Where "r" is the growth rate (in decimal form), "t" is the number of times intervals and this is the initial amount:
[tex]P_0[/tex]1. In this case, from 8:00 A.M to 5:00 P.M. you know that:
[tex]\begin{gathered} P=1100 \\ t=9 \end{gathered}[/tex]And the initial amount is:
[tex]P_0=300[/tex]2. Then, you can substitute values into the equation and solve for "r", in order to find its value:
[tex]\begin{gathered} P=P_0e^{rt} \\ \\ 1100=300\cdot_{}e^{r(9)} \end{gathered}[/tex][tex]\frac{1100}{300}=e^{9r}[/tex]Remember the following properties:
[tex]\begin{gathered} ln(a)^m=m\cdot\log (a)^{} \\ \\ \ln (e)=1 \end{gathered}[/tex]Then taking Natural Logarithm on both sides and simplifying, you get:
[tex]\begin{gathered} \ln (\frac{1100}{300})=\ln (e)^{9r} \\ \\ \ln (\frac{1100}{300})=9r\cdot\ln (e) \\ \\ \ln (\frac{1100}{300})=9r(1) \\ \\ \ln (\frac{1100}{300})=9r \\ \\ \frac{\ln (\frac{1100}{300})}{9}=r \end{gathered}[/tex][tex]r\approx0.1444[/tex]3. From 8:00 A.M. to 8:00 A.M in the next morning, there are 24 hours. Then, you can say that:
[tex]\begin{gathered} P_0=300 \\ r\approx0.1444 \\ t=24 \end{gathered}[/tex]Now you can substitute values and find the number of bacteria at 8:00 A.M of the next morning:
[tex]\begin{gathered} P=P_0e^{rt} \\ \\ P=300\cdot e^{(0.1444)(24)} \\ \\ P=300\cdot e^{(3.4656)} \end{gathered}[/tex][tex]P\approx9599[/tex]Hence, the answer is:
[tex]P\approx9599[/tex]
Convert the following equation from Standard Form to Slope-Intercept Form. 6x-3y=4 *
The slope-intercept form is y=mx+b, where "m" is the slope and "b" is the y-intercept.
So what we need to do is to clear "y" in a positive way as follows:
[tex]\begin{gathered} 6x-3y=4 \\ 3y=6x-4 \\ y=\frac{6x-4}{3} \\ y=\frac{6x}{3}-\frac{4}{3} \\ y=2x-\frac{4}{3} \end{gathered}[/tex]In conclusion, The Standard Form to Slope-Intercept Form is:
[tex]y=2x-\frac{4}{3}[/tex]What is the solution to × + 12 = 25?A. × = 12B. × = 24C. × = 13D. × = 37
The given equation is
[tex]x+12=25[/tex]Subtract 12 from each side.
[tex]\begin{gathered} x+12-12=25-12 \\ x=13 \end{gathered}[/tex]Hence, the answer is C.A box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys. If you are first to the box and grab 3 jerseys what is the probability that you randomly grab 3 extra-large jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Given:
A box of jerseys for a pick-up game of basketball contains:
8 extra-large jerseys,
6 large jerseys,
4 medium jerseys.
The total number of jerseys = 8 + 6 + 4 = 18
So, the probability to grab 3 extra-large jerseys will be =
[tex]\frac{8}{18}=\frac{2\cdot4}{2\cdot9}=\frac{4}{9}[/tex]We can exoress the answer as a decimal rounded to the nearest millinth : 0.444444
Write a definition for the function that best describes this graph.
Given the points on the graph:
(x, y) ==> (-1, 2), (0, 0), and (3, 1)
The graph represents a piece-wise function.
Let's write a definition for the function that best describes the graph.
Using the points, we have:
• (-1, 2) ==> f(x) = 2, when x = -1
,• (3, 1) ==> f(x) = 1, when x = 3
Let's find the equation of each line.
• Equation of line segment with endpoints (-1, 2) and (0, 0)
Apply the slope intercept form:
y = mx + b
Use the slope formula to find the slope:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x2} \\ \\ m=\frac{0-2}{0-(-1)}=\frac{-2}{1}=-2 \end{gathered}[/tex]Therefore, the equation is:
y = -2x
• Equation of line segments with endpoints (3, 1) and (0, 0);
[tex]m=\frac{0-1}{0-3}=\frac{-1}{-3}=\frac{1}{3}[/tex]Therefore, the equation is:
y = 1/3x
Hence, the definition for the functions that best describe the left piece of the graph is:
f(x) = -2x, if -1 ≤ x ≤ 0
The definition for the right piece of the function is:
f(x) = 1/3x, if 0 ≤ x ≤ 3
ANSWER:
f(x) = -2x, if -1 ≤ x ≤ 0
Lashonda needs to memorize words on a vocabulary list for Russian class. She has memorized 22 of the words, which is one-half of the list. How many wordsare on the list?
ANSWER
44 words
EXPLANATION
Let 'x' be the number of words in the list. We know that half the list is 22 words:
[tex]\frac{1}{2}x=22[/tex]To find x we just have to multiply both sides of the equation by 2:
[tex]\begin{gathered} \frac{1}{2}\cdot2x=22\cdot2 \\ x=44 \end{gathered}[/tex]There are 44 words on the list.
6Consider the line y=-=x+2Find the equation of the line that is perpendicular to this line and passes through the point (-6, 4).Find the equation of the line that is parallel to this line and passes through the point (-6, 4).Note that the ALEKS graphing calculator may be helpful in checking your answer.Hey
SOLUTION
For a line to be perpendicular to another line, product of thier gradient must be -1.
if the gradient is given as
[tex]\begin{gathered} m_{1\text{ }}andm_{2\text{ }},\text{ then} \\ m_1m_{2=-1} \end{gathered}[/tex]Then given the line
[tex]y=\frac{6}{7}x+2[/tex]The gradient of the line is the coefficient of x using the expression
[tex]\begin{gathered} y=mx+c \\ m=Gradient \end{gathered}[/tex]Hence, we have
[tex]m_1=\frac{6}{7}[/tex]Then, using
[tex]\begin{gathered} m_1m_2=-1 \\ m_2=\frac{-1}{m_1} \\ m_2=-1\times\frac{7}{6}=-\frac{7}{6} \end{gathered}[/tex]Given the point (-6,4), the line perpendicular will be having the equation
[tex]\begin{gathered} y-y_1=m_2(x-x_1) \\ \text{where }y_1=4\text{ and x}_1=-6 \end{gathered}[/tex]Then we obtain
[tex]\begin{gathered} y-4=-\frac{7}{6}(x-(-6)) \\ y-4=-\frac{7}{6}x-7 \\ y=-\frac{7}{6}x-7+4 \\ y=-\frac{7}{6}x-3 \end{gathered}[/tex]Therefore the equation perpendicular to this line is given as y=-7/6x - 3
[tex]y=-\frac{7}{6}x-3[/tex]Then the equation parallel to the same line will have the same gradient
[tex]m_1=m_2=\frac{6}{7}[/tex]Then the equation parallel passing through the point (-6,4) will be
[tex]\begin{gathered} y-4=\frac{6}{7}(x-(-6)) \\ y-4=\frac{6}{7}(x+6) \\ y-4=\frac{6}{7}x+\frac{36}{7} \\ y=\frac{6}{7}x+\frac{36}{7}+4 \\ y=\frac{6}{7}x+\frac{64}{7} \end{gathered}[/tex]The equation of the line that is parallel to this line and passes through the point (-6, 4) will be y=6/7x+64/7
[tex]y=\frac{6}{7}x+\frac{64}{7}[/tex]
I need help!! I looked at my notes & nothing.
To solve x;
1. Mulriply both sides of the equation by the denominator of the fraction in the right:
[tex]\begin{gathered} L*\sqrt{8-2x-x^2}=\frac{1}{\sqrt{8-2x-x^2}}*\sqrt{8-2x-x^2} \\ \\ L*\sqrt{8-2x-x^2}=1 \end{gathered}[/tex]2. Divide both sides of the equation into L:
[tex]\begin{gathered} \frac{L*\sqrt{8-2x-x^2}}{L}=\frac{1}{L} \\ \\ \sqrt{8-2x-x^2}=\frac{1}{L} \end{gathered}[/tex]3. Square both sides of the equation:
[tex]\begin{gathered} (\sqrt{8-2x-x^2})^2=(\frac{1}{L})^2 \\ \\ 8-2x-x^2=\frac{1}{L^2} \end{gathered}[/tex]4. Rewrite the term in the right with a negative exponent:
[tex]8-2x-x^2=L^{-2}[/tex]3. Rewrite the equation in the form ax^2+bx+c=0
[tex]-x^2-2x+8-L^{-2}=0[/tex]Use the quadratic formula to solve x:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} a=-1 \\ b=-2 \\ c=8-L^{-2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt{(-2)^2-4(-1)(8-L^{-2})}}{2(-1)} \\ \\ x=\frac{2\pm\sqrt{4+4(8-L^{-2})}}{-2} \\ \\ x=-\frac{2\pm\sqrt{4+4(8-L^{-2})}}{2} \end{gathered}[/tex]Answer:[tex]x=\frac{-2\pm\sqrt{4+4(8-L^{-2})}}{2}[/tex]If a restaurant's gross receipts for one week total $12,000, of which $8,000 is profit, what percent of the gross receipts is profit?
EXPLANATION
Let's see the facts:
Gross receipts = $12,000
Profit = $8,000
The percentage can be obtained by applying the following relationship:
[tex]\text{Profit\%}=\frac{profit}{\text{gross receipts}}\cdot100=\frac{8,000}{12,000}\cdot100=66.7\text{ \%}[/tex]The answer is 66.7%
Find the equation of the tangent line to the function
Compute the slope of f(x):
[tex]f(x)=\frac{20}{x^2}[/tex]For x = -2
[tex]f(-2)=\frac{20}{(-2)^2}=\frac{20}{4}=5[/tex]Find the line with slope m = 5 and passing through (-2,5):
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-5=5(x-(-2)) \\ y-5=5(x+2) \\ y-5=5x+10 \\ y-5+5=5x+10+5 \\ y=5x+15 \end{gathered}[/tex]Answer: equation of the tangent line is y = 5x + 15
Olive's garden is only 10yd² and the watermelon plants she wants to grow require 2.5yd² each. How many watermelon plants can she grow?
According to the information given in the exercise, you know that each watermelon plant requires and area of 2.5 square yards.
Let be "x" the number of watermelon plants that Olive can grow.
Knowing that her garden has an area of 10 square yards, you can set up the following proportion:
[tex]\frac{1}{2.5}=\frac{x}{10}[/tex]Therefore, you must solve for the variable "x" in order to find its value. To do this, you can apply the Multiplication property of equality by multiplying both sides of the equation by 10. Then, you get:
[tex]\begin{gathered} (10)(\frac{1}{2.5})=(\frac{x}{10})(10) \\ \\ \frac{10}{2.5}=x \\ \\ x=4 \end{gathered}[/tex]Then, the answer is: She can grow 4 watermelon plants.
Solve the following equations without the use of a model. Write all fractional answers in simplest form. Be sure to check your solutions.
So,
We're going to solve the following equation:
[tex]\frac{7}{2}p-\frac{11}{12}=\frac{5}{9}[/tex]The first thing we need to do, is to pass all the numbers (independent terms) to the other side of the equation, and let the variable p in the other side.
Notice that if we pass the numbers to the other side, they will pass with the opposite sign. Like this:
[tex]\frac{7}{2}p=\frac{11}{12}+\frac{5}{9}[/tex]Now we're going to sum the fractions:
[tex]\begin{gathered} \frac{7}{2}p=\frac{99+60}{108} \\ \\ \frac{7}{2}p=\frac{159}{108} \end{gathered}[/tex]Now, we just multiply the denominator to the other side, and divide by the numerator:
[tex]p=\frac{159\cdot2}{108\cdot7}=\frac{318}{756}[/tex]Simplifying, we got that:
[tex]p=\frac{53}{126}[/tex]Example:
Suppose you have the equation:
[tex]x-1=2[/tex]We are looking for let the variable "x" alone in a side of the equation, so, to do this we could sum "1" to both sides:
[tex]\begin{gathered} x-1+1=2+1 \\ x=3 \end{gathered}[/tex]The same thing happens in this problem.
1Let's find-12.First, write the addition so the fractions have denominator 12.Then add.=1+-12- +4=1212Х5?
Given:
[tex]\frac{1}{4}+\frac{1}{12}[/tex]Making the denominator 12.
[tex]\text{ We know that 4}\times3=12.[/tex][tex]\frac{1}{4}+\frac{1}{12}=\frac{1\times3}{4\times3}+\frac{1}{12}[/tex][tex]\frac{1}{4}+\frac{1}{12}=\frac{3}{12}+\frac{1}{12}[/tex]Add the numerator.
[tex]\frac{1}{4}+\frac{1}{12}=\frac{3+1}{12}[/tex][tex]\frac{1}{4}+\frac{1}{12}=\frac{4}{12}[/tex]Simplify.
[tex]\frac{1}{4}+\frac{1}{12}=\frac{1}{3}[/tex]Hence the answer is
[tex]\frac{1}{4}+\frac{1}{12}=\frac{3}{12}+\frac{1}{12}=\frac{1}{3}[/tex]the data show a negative/ positive correlation.the data show no causation/ causation.PLEASE HELP
From the observation, the data show a positive correlation because as chemistry increase geography increase
The data show causation because a change in chemistry value increases geography also increases and a change in chemistry decreases, geography also decreases in value.
Summary,
The data shows a positive correlation.
The data show causation.
PLEASE HELP!!!!! No Links!!! IM FAILING MATH, NEED TO PASS ASAP!
102 and x are vertical angles so they measure the same.
x = 102°
The third option is the correct choice.
12, 42, 72, 102..... Recursive Formula an = 12 * 30n-1 an = an-1 -12 an = 12 + 30 (n - 1 )an = an-1 + 12
Observe that the difference of the sequence is 30. The first term is 12.
Let's use the arithmetic sequence formula
[tex]a_n=a_1+(n-1)d[/tex]Replacing the given information, we have.
[tex]\begin{gathered} a_n=12+(n-1)\cdot30 \\ a_n=12+30n-30 \\ a_n=30n-18 \end{gathered}[/tex]Hence, the right answer is C because it relates correctly the first term and the difference.Can you use a proportion to solve for the length of a segment when an altitude is drawn in a right triangle
Here, we want to use proportion to solve for the length of the altitude x
y=0.5e^-2.5xfind the decay rate
The general exponential model is given in the form:
[tex]y=ae^{kt}[/tex]where y is the value at time t, a is the initial value, k is the growth/decay rate, and t is the time.
Note that if k is greater than 0, it represents a growth function, while if k is less than 0, the function represents a decay model.
From the question, the function is given to be:
[tex]y=0.5e^{-2.5x}[/tex]This means that we have the following parameters:
[tex]\begin{gathered} a=0.5 \\ k=-2.5 \end{gathered}[/tex]Therefore, the decay rate is -2.5.
