Answers
Answer:
3
Step-by-step explanation:
In parallelogram, opposite sides are equal.
Here,
5x + 2 and 17 are opposite sides.
5x + 2 = 17
5x = 17 - 2
5x = 15
x = 15 / 5
x = 3
The equation should look like this:
5x + 2 = 17
Why 17? Because if you look at the opposite side of the parallelogram, you can see a parallel line that is the exact same length. Since it also isn’t an equation, we can tell this would be the true length of it.
Okay, to solve it, first subtract 2 on both sides of the equation. Why? Because on the left side of the equation (the numbers before the equal sign) we can see that there is one coefficient (number with a variable) and one constant (just a plain number). In equations like this, you want only coefficients or constants per side. To remove the constant from the left side, do the inverse of the number. Always remember that whatever you do on one side, has to be done to the other.
5x + 2 - 2 = 17 - 12
This equals:
5x = 15
Now, just divide by the coefficient, in this case 5, on both sides. This removes the 5.
5x/5 = 15/5
This leaves:
x = 3
Related Questions
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Equation 1
Equation 2
Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married
American adults, y, x years after 1970. Use these models to complete parts a and b.
a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For
that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group?
In year
the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of
Americans will belong to each group.
Answers
After 4 years the percentage of never-married adults will be the same as the percentage of married adults.
The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Multiply the second equation with 3
-3x + 10y = 160 .....equation 1
3x + 6y = 492........equation 2
adding equation 1 and 2
16y = 652
y = 40.75
x + 2y = 164
x = 164 - 2 (40.75)
x = 82.5
Let the number of years be t
-3x+10y x t = x+2y
t = 4x - 8y
t = 330 - 326
t = 4 years
Therefore, after 4 years the percentage of never-married adults will be the same as the percentage of married adults.
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Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer: y = -3x - 21
Step-by-step explanation:
Slope intercept form: y = mx + b
m is the slope, and b is the y-intercept.
y + 8 = -3(x + 7)
Start by distributing -3 into the parenthesis.
y + 8 = -3x - 21
subtract 8 from both sides to get the final answer.
y = -3x - 29
Answer:
Slope-intercept form,
y = -3x - 29Step-by-step explanation:
Now we have to,
→ Rewrite the given equation in the slope-intercept form.
The slope-intercept form is,
→ y = mx + b
The equation is,
→ y + 8 = -3(x + 7)
Then the value of y will be,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Hence, answer is y = -3x - 29.
If A=(-7,8,1) and B(8,7,7), find ||AB||. Round to 3 decimal places
Answers
Given,
A= (-7, 8, 1).
B= (8, 7, 7)
The value of ||AB|| is,
[tex]\begin{gathered} \mleft\Vert AB\text{ }\mleft\Vert\text{ = }A.B\mright?\mright? \\ \end{gathered}[/tex]The value of A.B is ,
[tex]\begin{gathered} A\mathrm{}B=(-7.8+8.7+1.7) \\ AB=(-56+56+7) \\ AB=7 \end{gathered}[/tex]Hence, the value is 7.
The statement listed below is false. Let p represent the statement.
Answers
We will have that the negation of the statement would be:
*That product did not emerge as a toy in 1949. [Option B]
Lemons are sold in bag of six lemons for four dollars If you bought 24 how much would you spend
Answers
Lemons cost $4 for a bag of six, so using the unitary method, which states, "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons.
What is Unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.
Here,
Let x be the cost of 24 lemons.
6 lemons for $4
24 lemons for $x
by unitary method,
cost of 1 lemon=$4/6
cost of 24 lemons,
=24*(4/6)
=$16
Using the unitary method, which states that "The unitary method is a process of finding the value of a single unit, and based on this value; we can find the value of the required number of units," $16 will be spent for 24 lemons since a bag of six costs $4.
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Consider the functions below.Represent the interval where both functions are increasing on the number line provided.
Answers
The function f(x) is increasing for the intervals:
[tex]\begin{gathered} x\in(-\infty,-2\rbrack \\ x\in\lbrack2,\infty) \end{gathered}[/tex]how do I do domin and range on a graph
Answers
Consider that the domain are the set of x values with a point on the curve.
In this case, based on the grap, you can notice that the domain is:
domain = (-8,2)
domain = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2}
In this case you can observe that the circle has a left limit given by x = -8 (this can be notices by the subdivisions of the coordinate system) and a right limit given by x = 2. That's the reason why it is the interval of the domain.
The range are the set of y values with a point on the curve.
range = (-3,7)
range = {-3,-2,-1,0,1,2,3,4,5,6,7}
In this case, you observe the down and up limits of the circle.
Find the area of the shaded circles. Leave your answer in terms of pi or round to the nearest 10th
Answers
step 1
Find out the area of the complete circle
[tex]A=\pi\cdot r^2[/tex]we have
r=10 units
substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]Remember that the area of the complete circle subtends a central angle of 360 degrees
so
Applying proportion
Find out the area of the circle with a central angle of 330 degrees
100pi/360=x/330
solve for x
x=(100pi/360)*330
x=91.67pi unit2Graph the parabola. I have a picture of the problem
Answers
Let's begin by listing out the given information
[tex]\begin{gathered} y=(x-3)^2+4 \\ y=(x-3)(x-3)+4 \\ y=x(x-3)-3(x-3)+4 \\ y=x^2-3x-3x+9+4 \\ y=x^2-6x+13 \\ \\ a=1,b=-6,c=13 \end{gathered}[/tex]The vertex of the function is calculated using the formula:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-6}{2(1)}=\frac{6}{2}=3 \\ x=3 \\ \\ y=(x-3)^2+4 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ \\ (x,y)=(h,k)=(3,4) \end{gathered}[/tex]For the function, we assume values for x to solve. We have:
[tex]\begin{gathered} y=(x-3)^2+4 \\ x=1 \\ y=(1-3)^2+4=-2^2+4=4+4 \\ y=8 \\ x=2 \\ y=(2-3)^2+4=-1^2+4=1+4 \\ y=5 \\ x=3 \\ y=(3-3)^2+4=0^2+4=0+4 \\ y=4 \\ x=4 \\ y=(4-3)^2+4=1^2+4=1+4 \\ y=5 \\ x=5 \\ y=(5-3)^2+4=2^2+4=4+4 \\ y=8 \\ \\ (x,y)=(1,8),(2,5),(3,4),(4,5),(5,8) \end{gathered}[/tex]We then plot the graph of the function:
Lana draws ALMN on the coordinate plane. What is the perimeter of ALMN? Round to the nearest unit
Answers
We are asked to determine the perimeter of triangle LMN. To do that we will use the fact that the perimeter is the sum of the length of the sides of the triangle. Therefore, we have:
[tex]P=LM+MN+LN[/tex]To determine the value of the length of "LM" we will use the formula for the euclidian distance:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)_;\left(x_2,y_2\right) \\ \end{gathered}[/tex]Are the endpoints of the segment. For LM we have that the coordinates of the endpoints are:
[tex]L=\lparen-3,2)[/tex][tex]M=(3,5)[/tex]Substituting we get:
[tex]d_{LM}=\sqrt{(3-(-3))^2+(5-2)^2}[/tex]Solving the operations:
[tex]d_{LM}=\sqrt{6^2+3^2}[/tex]Solving the operations:
[tex]d_{LM}=\sqrt{45}[/tex]Now, we use the endpoints of MN:
[tex]M=(3,5)[/tex][tex]N=(9,2)[/tex]Substituting we get:
[tex]d_{MN}=\sqrt{(9-3)^2+(2-5)^2}[/tex]Solving the operations we get:
[tex]\begin{gathered} d_{MN}=\sqrt{6^2+\left(-3\right)^2} \\ \\ d_{MN}=\sqrt{45} \end{gathered}[/tex]Now, we apply the equation for segment LN:
[tex]d_{LN}=\sqrt{}(9-(-3))^2+(2-2)^2[/tex]Solving the operations:
[tex]d_{LN}=12[/tex]Now, we substitute in the formula for the perimeter:
[tex]P=\sqrt{45}+\sqrt{45}+12[/tex]Adding like terms:
[tex]P=2\sqrt{45}+12[/tex]In decimal form rounded to the nearest unit this is:
[tex]P=25[/tex]Therefore, the perimeter of the figure is 25.
Can you please help me solve this and the test statistics and p value
Answers
The claim is that the population mean for the smartphone carrier's data speed at airports is less than 4.00 Mbps
The parameter of the study is the population mean, symbolized by the Greek letter mu "μ"
The researchers believe is that his value is less than 4, you can symbolize this as:
[tex]\mu<4[/tex]This expression does not include the "=" symbol, which indicates that it represents the alternative hypothesis. The null and alternative hypotheses are complementary, so if the alternative hypothesis represents the values of μ less than 4, then the null hypothesis, as its complement, should represent all other possible values, which are those greater than and equal to 4. You can represent this as:
[tex]\mu\ge4\text{ or simply }\mu=4[/tex]The statistical hypotheses for this test are:
[tex]\begin{gathered} H_0\colon\mu=4 \\ H_1\colon\mu<4 \end{gathered}[/tex]Option A.
In the display of technology, you can see the data calculated for the test.
The second value shown in the display corresponds to the value of the test statistic under the null hypothesis, you have to round it to two decimal places:
[tex]t_{H0}=-2.432925\approx-2.43[/tex]The value of the test statistic is -2.43
The p-value corresponds to the third value shown in the display.
The p-value is 0.009337
To make a decision over the hypothesis test using the p-value you have to follow the decision rule:
- If p-value ≥ α, do not reject the null hypotheses.
- If p-value < α, reject the null hypotheses.
The significance level is α= 0.05
Since the p-value (0.009337) is less than the significance level of 0.05, the decision is to reject the null hypothesis.
Conclusion
So, at a 5% significance level, you can conclude that there is significant evidence to reject the null hypothesis (H₀: μ=4), which means that the population mean of the smartphone carrier's data speed at the airport is less than 4.00 Mbps.
80.39 rounded to nearest whole number
Answers
Answer:
80
Step-by-step explanation:
It is 80 because .39 is not quite 4.
so in a instance like this you would round .39 to .4 and .4 cant be rounded up to .5 so it would go down because it is to the nearest whole number to instead of it being 81 ( if it could be rounded to 80.5 ), it goes to just 80.
One way to help with rounding is:
" 4 and below let it go
if its 5 and above give it a shove. " rugrat k aka rgr k
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if 5 is added eighteen times to a number the result is 174 what is the number
Answers
Answer
The number is 84.
Step-by-step Explanation
The question wants us to find a number that gives 174 when 5 is added to it eighteen times.
Let that number we are looking for be x.
Interpreting the question into a mathematical equation, we have
x + (5 × 18) = 174
x + 90 = 174
Subtract 90 from both sides
x + 90 - 90 = 174 - 90
x = 84
Hence, the number we are looking for, is 84.
Hope this Helps!!!
(a)If Diane makes 75 minutes of long distance calls for the month, which plan costs more?
Answers
Answer:
Step-by-step explanation:
huh the proper question
How do I solve this I do understand how to
Answers
Solve for the unknown variable using a pythagoras theorem:
Hypotenuse = 32+x
Opposite = 56
Adjacent = x
[tex]\begin{gathered} \text{Hyp}^2=\text{opp}^2+\text{adj}^2 \\ (32+x)^2=56^2+x^2 \\ (32+x)(32+x)=3136+x^2 \\ 1024+64x+x^2=3136+x^2 \\ \text{collect like terms} \\ 64x+x^2-x^2=3136-1024 \\ 64x=2112 \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} \frac{64x}{64}=\frac{2112}{64} \\ x=33 \end{gathered}[/tex]Therefore the correct value of x = 33
El contratista encargado de construir el
cerco perimetral desea saber la expresión
algebraica correspondiente al perímetro de
todo el lote
Medidas:
25p-8
40p+2
Answers
El perímetro del lote tiene una medida de 130 · p - 12 unidades.
¿Cuál es la longitud del cerco perimetral para un lote?
El perímetro es la suma de las longitudes de los lados de una figura, un rectángulo tiene cuatro lados, dos pares de lados iguales. En consecuencia, el perímetro del lote es el siguiente:
s = 2 · w + 2 · l
Donde:
w - Ancho del lote.l - Largo del lote.s - Perímetro del lote.Si sabemos que w = 25 · p - 8 y l = 40 · p + 2, entonces el perímetro del lote es:
s = 2 · (25 · p - 8) + 2 · (40 · p + 2)
s = 50 · p - 16 + 80 · p + 4
s = 130 · p - 12
El perímetro tiene una medida de 130 · p - 12 unidades.
ObservaciónNo se ha podido encontrar una figura o imagen asociada al enunciado del problema. Sin embargo, se puede inferir que el lote tiene una forma rectangular debido a las medidas utilizadas. En consecuencia, asumimos que la medida del ancho es igual a 25 · p - 8 unidades y del largo es igual a 40 · p + 2 unidades.
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Segment AC has a midpoint B. If AB = 2x - x - 42 andBCI_x+11x +21, find the length of Ac.
Answers
The equation for the segment AB is;
[tex]2x^2-x-42[/tex]The equation for the segment BC is ;
[tex]x^2+11x+21[/tex]If segment AC has midpoint at B , this means ;
AC = AB + BC
To get AC we add the equation for AB and BC
Performing addition as;
[tex]2x^2-x-42+x^2+11x+21[/tex]Collect like terms as;
[tex]2x^2+x^2+11x-x-42+21=AC[/tex][tex]3x^2+10x-21=AC[/tex]Answer
[tex]AC=3x^2+10x-21[/tex]
Omaha Beef Company purchased a delivery truck for $66,000. The residual value at the end of an estimated eight-year service life is expected to be $12,000. The company uses straight-line depreciation for the first six years. In the seventh year, the company now believes the truck will be useful for a total of 10 years (four more years), and the residual value will remain at $12,000. Calculate depreciation expense for the seventh year.
Answers
Given:
Company purchased = $66000
Find-:
Depreciation expense for the seventh year
Sol:
First, depreciate for 6 years using the regular method:
[tex]\begin{gathered} =\frac{\text{ Cost - salvage value}}{\text{ initial useful life}} \\ \\ =\frac{66000-12000}{8} \\ \\ =6750 \end{gathered}[/tex]The annual depreciation is 6750.
For 6 years
[tex]\begin{gathered} =6750\times6 \\ \\ =40500 \end{gathered}[/tex]So
[tex]\begin{gathered} \text{ Remaining useful life = 10-6} \\ =4 \\ \\ =\frac{66000-40500-12000}{4} \\ \\ =\frac{13500}{4} \\ \\ =3375 \end{gathered}[/tex]For seventh-year depreciation expense is $3375
Translate this phrase into an algebraic expression.72 decreased by twice a numberUse the variable n to represent the unknown number.
Answers
When the questions uses the word "decreased" this means that a value was subtracted by another value. The word "twice" symbolizes that a number was doubled or multiplied by 2. With this understanding, we can create the expression:
[tex]72-2n[/tex]If 1 centimeter equals 3 ft what is the actual length of the 5cm side of the yard?
Answers
this is
[tex]\begin{gathered} \frac{1}{3}=\frac{5}{x} \\ 1\times x=3\times5 \\ x=15 \end{gathered}[/tex]answer: 15 ft
Let h(t)=tan(4x + 8). Then h'(3) is
and h''(3) is
Answers
The most appropriate choice for differentiation will be given by
h'(3) = 24.02
h''(3) = [tex]210.48[/tex]
What is differentiation?
Differentiation is the process in which instantaneous rate of change of function can be calculated based on one of its variables.
Here,
h(x) = tan(4x + 8)
h'(x) = [tex]\frac{d}{dx} (tan(4x + 8))[/tex]
= [tex]sec^2(4x + 8)\frac{d}{dx}(4x + 8)[/tex]
= [tex]4sec^2(4x + 8)[/tex]
h'(3) =
[tex]4sec^2(4\times 3 + 8 )\\4sec^220\\24.02[/tex]
h''(x) =
[tex]\frac{d}{dx}(4sec^2(4x + 8))\\4\times 2sec(4x + 8)\times \frac{d}{dx}(sec(4x + 8))\\8sec(4x + 8)sec(4x+8)cosec(4x+8)\times\frac{d}{dx}(4x + 8)\\32sec^2(4x + 8)cosec(4x +8)[/tex]
h''(3) =
[tex]32sec^2(4\times 3+8)cosec(4\times 3+8)\\32sec^220cosec20[/tex]
[tex]210.48[/tex]
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Amelia used 6 liters of gasoline to drive 48 kilometers.How many kilometers did Amelia drive per liter?kilometers =At that rate, how many liters does it take to drive 1 kilometer?liters =
Answers
Answer:
8km /hr
1/ 8 of a litre.
Explanation:
We are told that Amelia drives 48 kilometres in 6 hours, this means the number of kilometres she drives per litre is
[tex]48\operatorname{km}\div6\text{litres}[/tex][tex]\frac{8\operatorname{km}}{\text{litre}}[/tex]Hence, Amelia drives 8 kilometres per litre.
The next question can be rephrased as, given that Amelia drives 8 km per litre, how many litres will it take to drive one kilometre?
To answer this question, we make use of the equation
[tex]\operatorname{km}\text{ travelled = 8km/litre }\cdot\text{ litres}[/tex]Now, we want
km travelled = 1 km
and the above equation gives
[tex]\begin{gathered} 1=\frac{8\operatorname{km}}{\text{litre}}\cdot\text{litres} \\ 1=8\cdot\text{litres} \end{gathered}[/tex]Dividing both sides by 8 gives
[tex]\text{litres}=\frac{1}{8}[/tex]Hence, it takes 1/8 of a litre to drive 1 kilometre.
Trying to solve this problem kind of having a hard time
Answers
Future Value of an Investment
The formula to calculate the future value (FV) of an investment P for t years at a rate r is:
[tex]FV=P\mleft(1+\frac{r}{m}\mright)^{m\cdot t}[/tex]Where m is the number of compounding periods per year.
Leyla needs FV = $7000 for a future project. She can invest P = $5000 now at an annual rate of r = 10.5% = 0.105 compunded monthly. This means m = 12.
It's required to find the time required for her to have enough money for her project.
Substituting:
[tex]\begin{gathered} 7000=5000(1+\frac{0.105}{12})^{12t} \\ \text{Calculating:} \\ 7000=5000(1.00875)^{12t} \end{gathered}[/tex]Dividing by 5000:
[tex]\frac{7000}{5000}=(1.00875)^{12t}=1.4[/tex]Taking natural logarithms:
[tex]\begin{gathered} \ln (1.00875)^{12t}=\ln 1.4 \\ \text{Operating:} \\ 12t\ln (1.00875)^{}=\ln 1.4 \\ \text{Solving for t:} \\ t=\frac{\ln 1.4}{12\ln (1.00875)^{}} \\ t=3.22 \end{gathered}[/tex]It will take 3.22 years for Leila to have $7000
True or false? Based only on the given information, it is guaranteed thatAD EBDADGiven: ADI ACDBICBAC = BCBCDO A. TrueB. FalseSUBMIT
Answers
According to the information given, we can assure:
For both triangles, two interior angles and the side between them have the same measure and length, respectively. This is consistent with the ALA triangle congruence criterion.
ANSWER:
True.
Need help Instructions: Find the measure of each angle Calculate the length of each side Round to the nearest tenth
Answers
Given,
The length of the perpendicular is 4.
The measure of the hypotenuse is 14.
Required:
The measure of each angle of the triangle.
As it is a right angle triangle,
The measure of angle C is 90 degree.
By using the trigonometric ratios,
[tex]\begin{gathered} cosA=\frac{AC}{AB} \\ cosA=\frac{4}{14} \\ A=cos^{-1}(\frac{4}{14}) \\ A=73.4^{\circ} \end{gathered}[/tex]By using the trigonometric ratios,
[tex]\begin{gathered} sinB=\frac{AC}{AB} \\ sinB=\frac{4}{14} \\ B=sin^{-1}(\frac{4}{14}) \\ B=16.6^{\circ} \end{gathered}[/tex]Hence, the measure of angle A is 73.4 degree, angle B is 16.6 degree and angle C is 90 degree.
Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 6 different colors. How many selections of collarsfor each of the 3 cats are possible if color repetitions are allowed
Answers
We will have the following:
Assuming that color repetitions can be made, then total number of selections for collars for the 3 cats will be:
[tex]6\ast6\ast6=216[/tex]So, there will be a total of 216 possible permutations of choices.
If the formula x=1/n, is used to find the mean of the following sample, what is the value of n? 2, 63, 88, 10, 72, 99, 38, 19
Answers
Given:
The formula is:
[tex]x=\frac{1}{n}\sum_{i=1}^nx_i[/tex]Series is:
[tex]2,63,88,10,72,99,38,19[/tex]Find-:
The value of "n"
Explanation-:
In the given formula "n" represent the number of member in a series.
Given series is:
[tex]2,63,88,10,72,99,38,19[/tex]The number of members is:
The members are 8.
So the value of "n" is:
[tex]n=8[/tex]The value of "n" is 8.
Answer: The answer to this problem is 6
Step-by-step explanation: i took the quiz, this is the correct answer.
Find the midpoint of the coordinates (3. -18) and (-5, -10) WHAT IS THE XVALUE?
Answers
Given the points (3, -18) and (-5, -10)
Let the midpoint of the given coordinates is (x , y)
[tex]x=\frac{3+(-5)}{2}=\frac{-2}{2}=-1[/tex][tex]y=\frac{(-18)+(-10)}{2}=\frac{-28}{2}=-14[/tex]So, the coordinates of the midpoint is (-1 , -14)
A coin is tossed nine times what is the probability of getting all tails express your answer as a simplified fraction or decimal rounded to four decimal places
Answers
The probability of getting a tail on each toss is:
[tex]\frac{1}{2}[/tex]Since there is only one way of getting all tails, it follows that the required probability is given by:
[tex](\frac{1}{2})^9\approx0.0020[/tex]Hence, the required probability is approximately 0.0020
Ashley can text 60 words in 45 seconds. At this rate, how many words can she text in 60 seconds?
Answers
Let Ashley can text x words in 60 minutes. Then equation for x is,
[tex]\begin{gathered} \frac{60}{45}=\frac{x}{60} \\ x=\frac{60\cdot60}{45} \\ =80 \end{gathered}[/tex]Thus, Ashley text 80 words in 60 seconds.