Answer:
Elimination isn't exactly the easiest for this situation. But since the equations are in the same form and not solved for the same variable, I would go with elimination. (If they were solved for the same variable, I would go with substitution.) It would require me to make a manipulation on both equations.
I would multiply first equation by 5 and second equation by -2. The reason I would do this is because the y's would have opposite coefficients and when you add opposites you get 0.
The new set of equations would look like this:
20x+10y=45
-14x-10y=2
But I will slope here since we aren't asked to solve it.
Some texts use the term linear combination instead of elimination. They are the same.
1. Two different quadratic functions have graphs with the same vertex. Which function graph increases faster between x=2 and x=3?
a. What is the vertex of each function graph?
b. What is the average rate of change in function a between x=2 and x=3?
c. What is the average rate of change in function B between x=2 and x=3?
d. Which function graph increases faster between x=2 and x=3?
Answer:
See below in bold.
Step-by-step explanation:
a. The vertex is at (2, -1) in both functions.
b. Function A : Rate of increase = (change in y values)/ (change in x values)
= (0 - (-1)) / (3-2)
= 1.
c. Function B : Rate of change =
(0.5 - (-1)) / (3-2)
= 1.5.
d. Function B increases faster between x = 2 and x = 3.
Answer:
A). (2, -1)
B). Average rate of change of function A = 1
C). Average rate of change of function B = 1.5
D). Graph of function B increases faster than function A.
Step-by-step explanation:
A). vertex of the function A will be (2, -1)
and vertex of the function B will be same as function A, (2, -1)
B). Average rate of change in function A between x = 2 and x = 3 will be
[tex]\frac{f(3)-f(2)}{x-x'}[/tex]
Equation of the function A will be f(x) = (x - 2)²-(-1)
f(x) = (x - 2)² + 1
f(3) = (3 -2)² + 1
= 1² + 1 = 2
f(2) = 0 + 1 = 1
Therefore, rate of change = [tex]\frac{2-1}{3-2}[/tex]=1
C). Average rate of change of function B will be
=[tex]\frac{f(3)-f(2)}{x-x'}[/tex]
=[tex]\frac{0.5+1}{3-2}[/tex] [ from the given table]
= 1.5
D).Since rate of change of graph B is greater than graph A therefore, function B will increase faster than function A.
Solve: In 2x + In 2 =0
Answer:
x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Using the rules of logarithms
• log x + log y ⇔ log(xy)
• [tex]log_{b}[/tex] = n ⇔ x = [tex]b^{n}[/tex]
Given
ln 2x + ln 2 = 0
ln(2x × 2) = 0
ln 4x = 0
4x = [tex]e^{0}[/tex] = 1 ( divide both sides by 4 )
x = [tex]\frac{1}{4}[/tex]
There are 6 cupcakes shared equally between 10 people. What fraction of a cupcake does each person receive?
A- six tenths cupcake
B- one tenth cupcake
C- ten sixths cupcake
D- one sixth cupcake
Answer:
six tenths cupcake
Step-by-step explanation:
6/1 ÷ 10/1
6/1 × 1/10 = 6/10
The fraction of a cupcake does each person receive will be [tex]\frac{6}{10}[/tex] i.e. option A, i.e. six tenths of cupcake.
What is fraction?The fraction is numerical representation of the numbers in the form of numerator and denominator.
We have,
Total cupcakes = 6
Total people = 10
So,
To get equal share of the cupcake divide it by total number of people,
i.e.
Equal share [tex]=\frac{Total\ cupcake}{Total\ people}[/tex]
So,
Equal share for 10 people [tex]=\frac{6}{10}[/tex]
So,
Everyone gets six tenths of cupcake.
Hence, we can say that the fraction of a cupcake does each person receive will be [tex]\frac{6}{10}[/tex] i.e. option A, i.e. six tenths of cupcake.
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Find the x-intercepts of the parabola with
vertex (-3,-14) and y-intercept (0,13).
Write your answer in this form: (x1,y1),(X2,y2).
If necessary, round to the nearest hundredth.
Answer:
(-0.84, 0) and (-5.16, 0).
Step-by-step explanation:
Which of the following is the equation for a circle with a radius of rand center
at (h, v)?
Answer:
[tex]\large\boxed{(x-h)^2+(y-v)^2=r^2-\bold{Standard\ form}}\\\boxed{x^2+y^2-2hx-2vy+h^2+v^2-r^2=0-\bold{General\ form}}[/tex]
Step-by-step explanation:
[tex](x-h)^2+(y-v)^2=r^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\x^2-2hx+h^2+y^2-2vy+v^2=r^2\qquad\text{subtract}\ r^2\ \text{from both sides}\\\\x^2+y^2-2hx-2vy+h^2+v^2-r^2=0[/tex]
eh best describes the range of the function
Which best describes the range of the function f(x)=2(1/4)x
after it has been reflected over the y-axis?
Answer:
(0,∞)
Step-by-step explanation:
The problems tells us to find the range of the function
f(x)=2*(1/4)^x
after it has been reflected over the y-axis
This means
g(x) = 2*(1/4)^(-x)
To quickly find the answer, we can plot the equation and examine the range in the graph.
The range of both functions is the same
(0,∞)
See attached picture
What is the measure of angle D?
52o
54o
57o
126o
For a given trapezium ABCD, measure of angle [tex]D = 52\°[/tex].
What is an angle?" An angle is defined as when two rays meet at a common point known as vertex."
According to the question,
Given trapezium ABCD,
Measure of angle [tex]BAD= 128\°[/tex]
Measure of angle [tex]ABC= 126\°[/tex]
Measure of angle [tex]BCD= 54\°[/tex]
Sum of all the interior angles in a trapezium is equal to [tex]360\°[/tex].
Therefore,
[tex]\angle ABC + \angle BCD +\angle CDA + \angle DAB = 360\°\\\\\implies 126\°+54\°+ \angle CDA + 128\°=360\°\\\\\implies \angle CDA = 360\° - 308\°\\\\\implies \angle CDA = 52\°[/tex]
Hence, Option (A) is the correct answer.
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prove that (x-2)is factor of p (x)=2x³-3x²-17x+30
Answer:
P(2)=0 then x-2 is a factor of P(x)
Step-by-step explanation:
To see if (x-2) is a factor just plug in 2 for x into the polynomial expression.
2(2)^3-3(2)^2-17(2)+30
2(8)-3(4)-34+30
16-12-34+30
4-34+30
-30+30
0
Since P(2)=0 then x-2 is a factor
Use the property of exponents to rewrite the expression
(-4qr)(-4qr)(-4qr)(-4qr)
Answer:
(-4qr)^4
Step-by-step explanation:
(-4qr)(-4qr)(-4qr)(-4qr)
There are 4 sets of -4qr being multiplied together
(-4qr)^4
Two cylinders with different radii have the same
volume.
Which statement is true?
A.
The bases of the two cylinders must have the
same areas.
B.
The cylinder with the smaller radius must be
taller.
C.
The cylinder with the larger radius must be
taller.
D.
The heights of the two cylinders must be
equal.
7. If the value of x varies directly with the value of y, and x = 3 when y = 21. What is the valu
y, and x = 3 when y = 21. What is the value of x when y =
105?
Answer:
15
Step-by-step explanation:
Because x=y÷7
i.e,105÷7=15
Please please help me
Answer:
multiply 2/5 by 4
Step-by-step explanation:
When we divide fractions, we use copy dot flip
2/5 ÷ 1/4
Copy dot flip
2/5 * 4/1
For this case we must find the quotient of the following expression:
[tex]\frac {\frac {2} {5}} {\frac {1} {4}} =[/tex]
Applying double C we have:
[tex]\frac {2 * 4} {5 * 1} = \frac {8} {5}[/tex]
This is equivalent to multiplying the following: [tex]\frac {2} {5} * 4 = \frac {8} {5}[/tex]
Answer:
OPTION A
Substitute t=3 and t=5 to determine if the two expressions are equivalent. 4(t+3) 4t+12 Which statements are true? Check all that apply. The value of both expressions when t=3 is 32. The two expressions are not equivalent. The value of both expressions when t=5 is 15. The value of both expressions when t=5 is 23. The two expressions are equivalent. The value of both expressions when t=3 is 24.
Answer:
Answers are:
The value of both expressions when t=3 is 32.
The the value of both expressions when t=3 is 24.
The two expressions are equivalent.
Step-by-step explanation:
These answers are 100% correct. I just finished my quiz. I hope this helps
Please mark me brainlyest :)
The correct statements are that, both the equations are equivalent when the value of t is taken 3 and The value of both the equations is 24 when t is taken as 3.
So, the correct options that match the statement above are E and F.
Simplification of expressions. Taking the value of t as 3 in both the equations, we get,[tex]4(t+3)\\\\4(3+3)\\\\\\4\ \rm x\ 6=24[/tex]Now, in the second expression, [tex]4t+12\\\\4\ \rm x\ 3+12\\\\12+12=24[/tex] Whereas, when the value of t is taken as 5 the values obtained are as 23 and 32 respectively.Hence, the correct options are E and F that the equations are of both the values when t is 3 is obtained as 24. And both the expressions are equivalent when t is taken as 3.
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Given trapezoids QRST and WXYZ, which statement explains a way to determine if the two figures are similar?
A. Verify corresponding pairs of sides are congruent by translation.
B. Verify corresponding pairs of angles are proportional by translation.
C. Verify corresponding pairs of sides are proportional by dilation.
D. Verify corresponding pairs of angles are congruent by dilation.
the answer is C, all sides must be proportional to a specific factor, or the dilation
Similar shapes may or may not be congruent.
The true statement is: (c) Verify corresponding pairs of sides are proportional by dilation.
From the question, we understand that:
QRST and WXYZ are similar
The possible scenarios are:
QRST ans WXYZ are congruentQRST ans WXYZ are not congruentThe best way to determine their similarities is to assume that they are not congruent
This means that, the trapezoids are dilated, and they must have proportional corresponding sides.
The above highlight means that:
Option (c) is true
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Which value of x is a solution of the inequality?
4x+7≥35
x = 6
x = 7
x = 3
x = 0
Answer:
x = 7
Step-by-step explanation:
Just try all the choices and see which one gives a valid answer
4x+7≥35
x = 6 : 4 (6) + 7 = 31 is NOT ≥35 (not valid)
x = 7 : 4 (7) + 7 = 35 IS ≥35 (valid) (ANSWER)
x = 3 : 4 (3) + 7 = 19 is NOT ≥35 (not valid)
x = 0 : 4 (0) + 7 = 7 is NOT ≥35 (not valid)
Answer:
x = 7
Step-by-step explanation:
Just try all the choices and see which one gives a valid answer
4x+7≥35
x = 6 : 4 (6) + 7 = 31 is NOT ≥35 (not valid)
x = 7 : 4 (7) + 7 = 35 IS ≥35 (valid) (ANSWER)
x = 3 : 4 (3) + 7 = 19 is NOT ≥35 (not valid)
x = 0 : 4 (0) + 7 = 7 is NOT ≥35 (not valid)
A hockey goalie blocks 75% of shots at the goal. How many shots can the goalie predict she or he will block in 75 tries
Answer:
56
Step-by-step explanation:
75% of 75 tries = 0.75×75 = 56.25
Rounding, he can expect to block 56 shots.
The equation y2/100+x2/4 =1 represents an ellipse. Which points are the vertices of the ellipse? (−10, 0) and (10, 0) (−2, 0) and (2, 0) (0, −10) and (0, 10) (0, −2) and (0, 2)
The vertices of the ellipse (10, 0), (-10, 0), (0, 10), and (0, -10) can be determined using the center and major axes of the ellipse.
Explanation:The vertices of the ellipse are at (10, 0), (-10, 0), (0, 10), and (0, -10). To find the vertices of an ellipse, you use the major and minor axes that pass through the center of the ellipse. In this case, the center is (4.619, 5.425), and the major axes are inclined at an angle of 128° 51' to the x-axis.
What are the points for f(x)=3^(x-1)-2
Answer: (0, -1 [tex]\frac{2}{3}[/tex]), (1, -1), (2, 1)
Step-by-step explanation:
Set the exponent equal to zero - that is your anchor point.
Then choose an x-value less than and greater than the anchor point.
[tex]\left\begin{array}{c|c|l}&\underline{\quad x\quad }&\underline{\qquad \qquad f(x)\qquad \qquad \qquad \quad }\\\text{less than anchor}&0&3^{0-1}-2=3^{-1}-2=\frac{1}{3}-2 = -1\frac{2}{3}}\\\\anchor\ point&1&3^{1-1}-2=3^{0}-2=1-2 = -1}\\\\\text{greater than anchor}&2&3^{2-1}-2=3^{1}-2=3-2 = 1}\end{array}\right[/tex]
in everyday English, interpret the financial meaning of the
y-intercept in the equation y=0.10x+9.50
Final answer:
The y-intercept in the equation y=0.10x+9.50 represents an initial financial value of $9.50, such as a fixed charge or baseline cost, before any variable amounts are factored in.
Explanation:
In everyday English, the financial meaning of the y-intercept in the equation y=0.10x+9.50 refers to the initial amount or fixed cost that does not depend on the quantity represented by x. In other words, when x, which might represent the quantity of goods sold or the number of hours worked, is zero, the y-intercept indicates a starting value of $9.50. This could be a baseline charge, a fixed fee, or some kind of initial cost before any additional variables are added to the equation.
What’s 0.85 in simplest form
Answer:
17/20
Step-by-step explanation:
To find the simplest form of 0.85 you need to turn it into a fraction.
To turn it into a fraction you put 85 over 100 since 0.85 is in the hundredths place.
85/100 can be simplified to 17/20 because 85/5 is 17 and 100/5 is 20
Answer:
17/20
Step-by-step explanation:
The simplest form of a number is a fraction. .85 as a fraction is 85/100. Simplifying this into 17/20 puts it into its simplest form.
Mateo is constructing an equilateral triangle inscribed in a circle with Center p . he draws the diameter of the circle through centerpiece using the Straight Edge next he opend his compass to a width equivalent to the radius of the circle what is his next step
Answer:
Step-by-step explanation:
Next he marks the circumference of the circle with 6 equal marks that also equal the radius.
He numbers the points consecutively.
He joins points 2 4 6 2 or 1 3 5 1 (The last point gets him back to where he started.
That's his equilateral triangle using just a straight edge and compass.
Help me I need to pass so I can go on to the next thing plz someone help me
Answer:
i cant see the picture
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
The scale factor is the ratio of the corresponding sides of the image to the original, that is
scale factor = [tex]\frac{CA'}{CA}[/tex] = [tex]\frac{4+16}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5
Factor the polynomial expression x6 – x3 – 20
Answer:
x6 − x3 − 20 = (x3)2 − x3 − 20 = (x3 + 4)(x3 − 5)
Step-by-step explanation:
In this trinomial, the exponent of the first term, 6, is double the exponent in the second term, 3. And, the third term contains no variables. So, we can factor the expression as we would a quadratic, but treating x3 as if it were x:
Answer:
(x³ - 5)(x³ + 4)
Step-by-step explanation:
Consider the factors of the constant term (- 20) which sum to give the coefficient of the x³ term (- 1)
The factors are - 5 and + 4, since
- 5 × 4 = - 20 and - 5 + 4 = - 1, hence
[tex]x^{6}[/tex] - x³ - 20 = (x³ - 5)(x³ + 4)
A pair of shoes coats $25 to make. This means that you need to charge a price of atleast __ just to cover you Options : A:$25 B:$10 C:$50
Answer:
25
Step-by-step explanation:
Because they cost $25 to make so in order to cover the cost they would need to charge at least 25, but out of those choices if they wanted to make a profit they'd need to charge the $50
Helaine graphed the equation 12x - 4y = 3. What was the slope of Helaine's line?
The slope of the graph is
Answer:
The slope of this line is 3.
Step-by-step explanation:
Solve 12x - 4y = 3 for y to obtain the equation in slope-intercept form:
Add 4y to both sides, obtaining 12x = 3 + 4y
Subtract 3 from both sides: 12x - 3 = 4y
Finally, divide all terms by 4: y = 3x - 3/4
The slope of this line is 3.
Answer: The slope of the graph is 3.
Step-by-step explanation:
The equation of a line in slope intercept for is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line.
The given equation of the line graphed by Helaine = [tex]12x - 4y = 3[/tex]
Now, rewrite the above equation in slope-intercept form by adding 4y and subtracting 3 from both sides , we get
[tex]4y=12x-3[/tex]
Divide 4 on both sides , we get
[tex]y=3x-\dfrac{3}{4}[/tex] which is the slope-intercept form.
[tex]\Rightarrow\text{Slope}=3[/tex]
Hence, the slope of Helaine's line =3
A triangle ABC has two side lengths of 28 ft. and 24 ft. If angle C is 91°, what's the measurement of angle B?
Answer:
B = 58.9
Step-by-step explanation:
We are given that a triangle ABC has two side lengths of 28 ft. and 24 ft. with angle C measuring 91°. We are to find the measure of angle B.
AB = 28 ft
AC = 24 ft
For this, we will use the sine formula:
[tex]\frac{sin B}{24} = \frac{sin91}{28}[/tex]
[tex]sin B = \frac{sin91 \times 24}{28}[/tex]
[tex] sin B = 0 . 8 5 7 [/tex]
[tex] B = sin' 0 . 8 5 7 [/tex]
B = 58.9
Help ASAP please! Thanks in advance.
In which set are ALL of the numbers solutions to the inequality x < -3?
Step-by-step explanation:
The second one, of course. Because the inequality means that x must be smaller than -3. So in negative numbers, numbers are getting smaller when they go far from 0. So [tex]-8\frac{2}{3},-6,-4, -3,5[/tex] are smaller than -3 because the distance between 0 and these numbers are more than he distance between zero and -3. Good luck :)
Square T was translated by the rule (x + 2, y + 2) and then dilated from the origin by a scale factor of 3 to create square T″. Which statement explains why the squares are similar?
A. Translations and dilations preserve side length; therefore, the corresponding sides of squares T and T″ are congruent.
B. Translations and dilations preserve orientation; therefore, the corresponding angles of squares T and T″ are congruent.
C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.
D. Translations and dilations preserve collinearity; therefore, the corresponding angles of squares T and T″ are congruent.
Answer: OPTION C.
Step-by-step explanation:
It is important to know the following:
Dilation:
Transformation in which the image has the same shape as the pre-image, but the size changes. Dilation preserves betweenness of points. Angle measures do not change.
Translation:
Transformation in which the image is the same size and shape as the pre-image. Translation preserves betweenness of points. Angle measures do not change.Therefore, since the Square T was translated and then dilated to create Square T'', we can conclude that the statement that explains why they are similar is:
Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.
Answer:
C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.
Step-by-step explanation:
please help i don know how to do this
thanks
Answer
The answer to this question is not one of your answer choices, but the answer is 240.1413932 square centimeters.
Step-by-step explanation:
A=πr(r+√h² + r²) [radical wrapped around h² + r²]
Find measure of angle A
Round to the nearest degree
To solve this question, we must use the cosine rule:
cos(A) = (b^2 + c^2 - a^2)/2bc, where A is the angle you want to find, a is the side opposite that angle, and b and c are the other two sides of the triangle.
Given that we know that a = 6, b = 12, c = 14, we can substitute these values into the formula to get:
cos(A) = (12^2 + 14^2 - 6^2)/2(12)(14)
cos(A) = (144 + 196 - 36)/336
cos(A) = 304/336
cos(A) = 19/21
A = cos-1(19/21)
A = 25° (to the nearest degree)