Answer:
2a - 5b = 1
3a + 5b = 14
Let's solve this system using elimination. Add the equations together to cancel the b-terms, then solve for a.
2a - 5b = 1
3a + 5b = 14
+___________
5a - 0 = 15
5a = 15
a = 3
Next, plug 3 for a into either of the equations and solve for b.
2a - 5b = 1
2(3) - 5b = 1
6 - 5b = 1
- 5b = -5
b = 1
Lastly, check all work by plugging both values for their respective variables.
2a - 5b = 1
2(3) - 5(1) = 1
6 - 5 = 1 -- This is true
3a + 5b = 14
3(3) + 5(1) = 14
9 + 5 = 14 -- This is true
The solution to the system of equations is (3, 1).
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
solve x^3-7x^2+7x+15
Step-by-step explanation:
\underline{\textsf{Given:}}
Given:
\mathsf{Polynomial\;is\;x^3+7x^2+7x-15}Polynomialisx
3
+7x
2
+7x−15
\underline{\textsf{To find:}}
To find:
\mathsf{Factors\;of\;x^3+7x^2+7x-15}Factorsofx
3
+7x
2
+7x−15
\underline{\textsf{Solution:}}
Solution:
\textsf{Factor theorem:}Factor theorem:
\boxed{\mathsf{(x-a)\;is\;a\;factor\;P(x)\;\iff\;P(a)=0}}
(x−a)isafactorP(x)⟺P(a)=0
\mathsf{Let\;P(x)=x^3+7x^2+7x-15}LetP(x)=x
3
+7x
2
+7x−15
\mathsf{Sum\;of\;the\;coefficients=1+7+7-15=0}Sumofthecoefficients=1+7+7−15=0
\therefore\mathsf{(x-1)\;is\;a\;factor\;of\;P(x)}∴(x−1)isafactorofP(x)
\mathsf{When\;x=-3}Whenx=−3
\mathsf{P(-3)=(-3)^3+7(-3)^2+7(-3)-15}P(−3)=(−3)
3
+7(−3)
2
+7(−3)−15
\mathsf{P(-3)=-27+63-21-15}P(−3)=−27+63−21−15
\mathsf{P(-3)=63-63}P(−3)=63−63
\mathsf{P(-3)=0}P(−3)=0
\therefore\mathsf{(x+3)\;is\;a\;factor}∴(x+3)isafactor
\mathsf{When\;x=-5}Whenx=−5
\mathsf{P(-5)=(-5)^3+7(-5)^2+7(-5)-15}P(−5)=(−5)
3
+7(−5)
2
+7(−5)−15
\mathsf{P(-5)=-125+175-35-15}P(−5)=−125+175−35−15
\mathsf{P(-5)=175-175}P(−5)=175−175
\mathsf{P(-5)=0}P(−5)=0
\therefore\mathsf{(x+5)\;is\;a\;factor}∴(x+5)isafactor
\underline{\textsf{Answer:}}
Answer:
\mathsf{x^3+7x^2+7x-15=(x-1)(x+3)(x+5)}x
3
+7x
2
+7x−15=(x−1)(x+3)(x+5)
\underline{\textsf{Find more:}}
Find more:
!!!!PLEASE HELP!!!!
What is the following quotient?
2
√13+ /11
O 13-2./11
13+ 11
6
13+ V11
12
√13 - 1
(D)
Step-by-step explanation:
Multiply and divide the fraction by the conjugate:
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}×\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]
[tex]= \dfrac{2(\sqrt{13} - \sqrt{11})}{(\sqrt{13})^2 - (\sqrt{11})^2}[/tex]
[tex]=\dfrac{2(\sqrt{13} - \sqrt{11})}{2}[/tex]
[tex]=\sqrt{13} - \sqrt{11}[/tex]
I need to know the answer ASAP
Answer:
Step-by-step explanation:
Form a polynomial whose zeros and degree are given,
Zeros: - 2, 2,7; degree: 3
Type a polynomial with integer coefficients and a leaning coefficient of 1 in the box below.
F(x)=
Answer:
if the zeros are x = -2, x = 0, and x = 1
then (x + 2), x and (x - 1) are factors of the polynomial
multiply these factors together
p(x) = x(x + 2)(x - 1)
p(x) = x(x2 + x - 2)
p(x) = x3 + x2 - 2x
this is a polynomial of degree 3 with the given roots
AB is tangent to the circle at B. M∠A = 27 and mBC=114 (The figure is not drawn to scale.)
9514 1404 393
Answer:
a. x = 60
b. y = 93
Step-by-step explanation:
The relevant relations are ...
external angle A is half the difference of intercepted arcs BC and BDinscribed angle y° is half the measure of intercepted arc CDthe sum of arcs of a circle is 360°__
Using these relations, we have ...
A = (BC -x°)/2
x° = BC -2A = 114° -2(27°)
x° = 60°
__
y° = CD/2 = (360° -BC -BD)/2 = (360° -114° -60°)/2
y° = 93°
x^{2} +y^{2} =?
cho mình hỏi với
Answer:
[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]
Step-by-step explanation:
[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]
Help. The graph shows the system of equations below.
2x -3y = -6
y = - 1/3x -4
9514 1404 393
Answer:
(a) The blue line ... solution ... (-6, -2)..
Step-by-step explanation:
The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.
The blue line represents the equation 2x -3y = -6.
The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.
I need help answering this ASAP
Answer:
"D"
if you multiply by Conjugate
the denominator would end up A^2 - b^2
the answer has 25 - 10x
that is D
Step-by-step explanation:
Oh Brian~
I need help again
Answer:
18c^3d^9
Step-by-step explanation:
2c^3 d^2 * 9d^7
We know that we add the exponents when the base is the same
2*9 c^3 d^(2+7)
18c^3d^9
Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)
Answer:
Step-by-step explanation:
There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).
How to estimate the point-slope form of an equation of the line through the points (-4, 7) and (5,-3)?Slope
[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
= (-3 - 7) / (5 - (-4))
= -10/9
The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).
y + 3 = (-10/9)(x - 5)
Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).
Therefore, the correct answer is y - 7 = (-10/9)(x + 4).
To learn more about the equation of a line refer to:
https://brainly.com/question/11751737
#SPJ2
Suppose that the distribution of snake lengths in a certain park is not assumed to be symmetric. According to Chebyshev's Theorem, at least what percentage of snake lengths are within k =2.9 standard deviations of the mean?
According to Chebyshev,
P(|X - µ| ≤ 2.9σ) ≥ 1 - 1/2.9² ≈ 0.8811
What is the measure of the angle in red?
70°
Answer:
See pic below.
Answer: C. 380°
Step-by-step explanation:
The following are on a parabola defining the edge of a ski
(-4, 1), (-2, 0.94), (0.1)
The general form for the equation of a parabola is:
Ax^2+ Bx +C= y
Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Repeat this process with 1 of the other to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.
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Answer:
a) 16A -4B +C = 1
b) 4A -2B +C = 0.94
c) C = 1
Step-by-step explanation:
Substitute the x- and y-values into the general form equation.
a. A(-4)² +B(-4) +C = 1
16A -4B +C = 1
__
b. A(-2)² +B(-2) +C = 0.94
4A -2B +C = 0.94
__
c. A(0)² +B(0) +C = 1
C = 1
_____
Additional comment
Solving these equations gives A=0.015, B=0.06, C=1. The quadratic is ...
0.015x² +0.06x +1 = y
log_c(A)=2
log_c(B)=5,
solve log_c(A^5B^3)
We know that [tex]\log_a(bc)=\log_a(b)+\log_a(c)[/tex].
Using this rule,
[tex]\log_c(A^5B^3)=\log_c(A^5)+\log_c(B^3)[/tex].
We also know that [tex]\log_c(a^b)=b\log_c(a)[/tex].
Using this rule,
[tex]\log_c(A^5)+\log_c(B^3)=5\log_c(A)+3\log_c(B)[/tex]
Now we know that [tex]\log_c(A)=2,\log_c(B)=5[/tex] so,
[tex]5\cdot2+3\cdot5=10+15=\boxed{25}[/tex].
Hope this helps :)
You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model (regression) sum of squares is 750. What is the adjusted R-squared value for this model
Answer:
Hence the adjusted R-squared value for this model is 0.7205.
Step-by-step explanation:
Given n= sample size=20
Total Sum of square (SST) =1000
Model sum of square(SSR) =750
Residual Sum of Square (SSE)=250
The value of R ^2 for this model is,
R^2 = \frac{SSR}{SST}
R^2 = 750/1000 =0.75
Adjusted [tex]R^2[/tex] :
[tex]Adjusted R^2 =1- \frac{(1-R^2)\times(n-1)}{(n-k-1)}[/tex]
Where k= number of regressors in the model.
[tex]Adjusted R^2 =1-(19\times 0.25/((20-2-1)) = 0.7205[/tex]
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the _____. a. coefficient of determination b. correlation coefficient c. confidence interval estimate d. standard error of the estimate
Answer:
coefficient of determination
Step-by-step explanation:
The Coefficient of determination, R² which is the squared value of the correlation Coefficient is used to give Tha proportion of variation in the predicted / dependent variable that can be explained by the regression line. The coefficient of determination ranges from 0 to 1. Once the proportion of explained variation is obtained, the proportion of unexplained variation is ( 1 - proportion of explained variation).
Another name for the standardized score from a normally distributed variable is the _____.
A. standard score
B. z-score
C. t-score
D. normal score
Answer:
the answer is b). z- score.
Answer:
b
Step-by-step explanation:
When a 0.42 tax was added to the price of a ticket, the total bill come to $7.03. Describe the above situation as a linear equation.
Answer:
P = 7.03 - 0.42T
Step-by-step explanation:
Let the price of a ticket be P.
Let the ticket be T.
A linear equation can be defined as an algebraic equation that's typically written for two (2) independent variables, in which each of them has an exponent of one (1) and they make a straight line when plotted on a graph.
Given the following data;
Tax = 0.42
Total bill = $7.03
Translating the word problem into an algebraic expression, we have;
0.42T + P = 7.03
P = 7.03 - 0.42T
A building 51 feet tall casts a shadow 48 feet long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue? Choose an answer
Answer: 17 feet
Step-by-step explanation:
51/48 = x/16
(51)(16)/48
The statute is 17 feet tall.
What are the similar triangles?Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.
What is the ratio of any two corresponding sides of similar triangles?The ratio of any corresponding sides in two equiangular triangles is always the same.
Let's visualize the situation according to the given question.
AB is the building ,whose height is 51f
BC is the shadow of the building AB, whose length is 48ft.
QR is the shadow of the tower statue, whose length is 16feet.
Let the height of the statue PR be h feet.
In triangle ACB and triangle PRQ
∠ACB = ∠PRQ = 90 degrees
( the objects and shadows are perpendicular to each other)
∠BAC = ∠QPR
( sunray falls on the pole and tower at the same angle, at the same time )
⇒ΔACB similar to ΔPRQ ( AA criterion)
Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.
⇒ AC/CB = PR/RQ
⇒[tex]\frac{51}{48} =\frac{h}{16}[/tex]
⇒ h = [tex]\frac{(51)(16)}{48}[/tex]
⇒ h = 17 feet.
Hence, the statute is 17 feet tall.
Learn more about the similar triangle here:
brainly.com/question/25882965
#SPJ2
find the area of the triangle
Answer:
75.03
Step-by-step explanation:
14×11×sin(77)
= 75.02649499..
≈ 75.03 (rounded to nearest hundredth)
Answered by GAUTHMATH
HELP PLEASE AND BE CORRECT
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Each point moves to 3 times its original distance from P.
A is 2 up and 1 left of P, so A' will be 6 up and 3 left of P.
B is 1 down and 2 left of P, so B' will be 3 down and 6 left of P.
C is 2 right of P, so C' will be 6 right of P.
Which of the following conversions is possible?
Meters to Liters
Feet to Miles
Pounds to Inches
Grams to Centimeters
Answer:
Feet to Miles
Step-by-step explanation:
Answer:
Feet to Miles
Step-by-step explanation:
Both units must measure the same quantity.
Smart phone: Among 239 cell phone owners aged 18-24 surveyed, 103 said their phone was an Android phone. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to at least three decimal places. The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is .
Answer:
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
Step-by-step explanation:
The point estimate is the sample proportion.
Sample proportion:
103 out of 249, so:
[tex]p = \frac{103}{249} = 0.4137[/tex]
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
Can someone help me? I don’t know how to solve the rest. I am struggling and I would be so happy if any of you helped me. Thank you for your help!
Which is the
Simplified form
r-7+s-12
Answer:
r + s - 19
General Formulas and Concepts:
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
r - 7 + s - 12
Step 2: Simplify
Combine like terms [constants]: r + s - 19Find the equation of the line passing through the point (-1,2)
and the points of intersections of the line 2x - 3y + 11 = 0 and
5x + y + 3 = 0
Answer:
[tex]y=-5x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
To solve for the equation of the line, we would need to:
Find the point of intersection between the two given linesUse the point of intersection and the given point (-1,2) to solve for the slope of the lineUse a point and the slope in [tex]y=mx+b[/tex] to solve for the y-interceptPlug the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation1) Find the point of intersection between the two given lines
[tex]2x - 3y + 11 = 0[/tex]
[tex]5x + y + 3 = 0[/tex]
Isolate y in the second equation:
[tex]y=-5x-3[/tex]
Plug y into the first equation:
[tex]2x - 3(-5x-3) + 11 = 0\\2x +15x+9 + 11 = 0\\17x+20 = 0\\17x =-20\\\\x=\displaystyle-\frac{20}{17}[/tex]
Plug x into the second equation to solve for y:
[tex]5x + y + 3 = 0\\\\5(\displaystyle-\frac{20}{17}) + y + 3 = 0\\\\\displaystyle-\frac{100}{17} + y + 3 = 0[/tex]
Isolate y:
[tex]y = -3+\displaystyle\frac{100}{17}\\y = \frac{49}{17}[/tex]
Therefore, the point of intersection between the two given lines is [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex].
2) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the two points [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex] and (-1,2):
[tex]m=\displaystyle \frac{\displaystyle\frac{49}{17}-2}{\displaystyle-\frac{20}{17}-(-1)}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{20}{17}+1}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{3}{17} }\\\\\\m=-5[/tex]
Therefore, the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-5x+b[/tex]
Plug in the point (-1,2) and solve for b:
[tex]2=-5(-1)+b\\2=5+b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
I hope this helps!
Please help me with this question
An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil. Out of 155 seeds planted in soil containing 3% mushroom compost by weight, 74 germinated. Out of 155 seeds planted in soil containing 5% mushroom compost by weight, 86 germinated. Can you conclude that the proportion of seeds that germinate differs with the percent of mushroom compost in the soil
Solution :
Let [tex]p_1[/tex] and [tex]p_2[/tex] represents the proportions of the seeds which germinate among the seeds planted in the soil containing [tex]3\%[/tex] and [tex]5\%[/tex] mushroom compost by weight respectively.
To test the null hypothesis [tex]H_0: p_1=p_2[/tex] against the alternate hypothesis [tex]H_1:p_1 \neq p_2[/tex] .
Let [tex]\hat p_1, \hat p_2[/tex] denotes the respective sample proportions and the [tex]n_1, n_2[/tex] represents the sample size respectively.
[tex]$\hat p_1 = \frac{74}{155} = 0.477419[/tex]
[tex]n_1=155[/tex]
[tex]$p_2=\frac{86}{155}=0.554839[/tex]
[tex]n_2=155[/tex]
The test statistic can be written as :
[tex]$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}[/tex]
which under [tex]H_0[/tex] follows the standard normal distribution.
We reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance, if the P-value [tex]<0.05[/tex] or if [tex]|z_{obs}|>Z_{0.025}[/tex]
Now, the value of the test statistics = -1.368928
The critical value = [tex]\pm 1.959964[/tex]
P-value = [tex]$P(|z|> z_{obs})= 2 \times P(z< -1.367928)$[/tex]
[tex]$=2 \times 0.085667$[/tex]
= 0.171335
Since the p-value > 0.05 and [tex]$|z_{obs}| \ngtr z_{critical} = 1.959964$[/tex], so we fail to reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance.
Hence we conclude that the two population proportion are not significantly different.
Conclusion :
There is not sufficient evidence to conclude that the [tex]\text{proportion}[/tex] of the seeds that [tex]\text{germinate differs}[/tex] with the percent of the [tex]\text{mushroom compost}[/tex] in the soil.
Using the following equation, find the center and radius: x2 −2x + y2 − 6y = 26 (5 points)
Answer:
Center: (1,3)
Radius: 6
Step-by-step explanation:
Hi there!
[tex]x^2-2x + y^2 - 6y = 26[/tex]
Typically, the equation of a circle would be in the form [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.
To get the given equation [tex]x^2-2x + y^2 - 6y = 26[/tex] into this form, we must complete the square for both x and y.
1) Complete the square for x
Let's take a look at this part of the equation:
[tex]x^2-2x[/tex]
To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:
[tex]x^2-2x+1[/tex]
Great! Now, let's add this to our original equation:
[tex]x^2-2x+1+y^2-6y = 26[/tex]
We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:
[tex]x^2-2x+1+y^2-6y = 26+1\\x^2-2x+1+y^2-6y = 27[/tex]
Complete the square:
[tex](x-1)^2+y^2-6y = 27[/tex]
2) Complete the square for y
Let's take a look at this part of the equation [tex](x-1)^2+y^2-6y = 27[/tex]:
[tex]y^2-6y[/tex]
To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:
[tex]y^2-6y+9[/tex]
Great! Now, back to our original equation:
[tex](x-1)^2+y^2-6y+9= 27[/tex]
Remember to add 9 on the other side as well:
[tex](x-1)^2+y^2-6y+9= 27+9\\(x-1)^2+y^2-6y+9= 36[/tex]
Complete the square:
[tex](x-1)^2+(y-3)^2= 36[/tex]
3) Determine the center and the radius
[tex](x-1)^2+(y-3)^2= 36[/tex]
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.
I hope this helps!
Answer:
[tex]\sqrt{g^2+f^2-c}[/tex]
[tex]g=-1,f=-3,c=-26[/tex]
so, the Center of the equation is [tex](1,3)[/tex]
Center → (1 , 3)[tex]\sqrt{(-1)^2+(-3)^2-(-26})[/tex]
[tex]=\sqrt{1+9+26}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
Radius → 6OAmalOHopeO
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
A) A = 100 + te^2
B) A = 100 + e^2t
C) A = 100e^2t
D) A = 100 + 2e^t
Answer:
D)
Step-by-step explanation: Im not so sure ok i sorry if Im wrong
