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The table shows a linear function. Write an equation that represents the function using function notation.
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Related Questions
MATH PLEASE HELP 50 POINTS 1 QUESTION
Complete the reasons in the proof below.
Given: ∠1 and ∠5 are supplementary.
Prove: a ∥ b
Statements
1. ∠1 and ∠5 are supplementary
2. ∠1 ≅ ∠2
3. ∠2 and ∠5 are supplementary
4. a ∥ b
Answers
For 2, due to that 1 and 2 are vertical angles (angles that are opposite to each other when two lines cross according to Math is Fun)
For 3, since ∠1=∠2, ∠1 can be substituted by ∠2 in ∠1+∠5=180 to get ∠2+∠5=180. Therefore, they are supplementary.
For 4, due to that we have Consecutive Interior Angles (they are angles that are on one side of a transversal, which is the line that cuts through a and b,but inside the two lines according to Math is Fun) adding up to 180 degrees, a || b
Feel free to ask if you have any questions!
The inequality x2 + 12x + 35 ≥ 0 has two critical points and three possible intervals for solutions. Choose each set of possible test points for the three intervals.
–8, –6, –4
–10, –6, 0
–6, 0, 6
–6, 0, 10
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-8,-6,-4
-10,-6,0
these are the possible test points for your three intervals
The given inequality is, x² + 12 x+35≥0
→ x²+7 x +5 x+5×7≥0
→ x (x+7) +5(x+7)≥0
→ (x+5)(x+7)≥0
→ x+5=0 ∧ x+7=0 gives x= -7 ∧ x= -5
Now drawing the number line and marking point ,-5 and -7 on it.
Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).
The solution set of inequality (x+5)(x+7)≥0 is (-∞ , -7] and [-5,∞).
The set of possible test points for
⇒ (-∞ , -7] → -8, -10
⇒ [-7,-5] → -6
⇒ [-5,∞) → -4, 0
Option (1) -8,-6,-4 and Option (2) -10,-6,0 satisfies the given condition.
Emily has 32 grams of a 25% sugar syrup, but this is just too sweet for her! How much pure water should she add to have a 10% syrup?
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original water content= 32*75/100=24 grams
original sugar content= 32*25/100= 8grams
total mass at 10% syrup:
8grams/total mass=10%=0.1
total mass=8/0.1=80grams
total mass of water=80grams- 8grams of sugar content= 72 grams
total mass of water added=72grams- 24grams original water content= 48grams.
answer: 48grams
25%+0%=10%
32g xg (32+x)g
Now, we create an equation:
(0.25^32)+(0^x)=0.1^(32+x)
8+0=3.2+0.1x
8=3.2+0.1x
4.8=0.1x
48=x
Answer: 48 gram.
An automobile manufacturing organization noted a drop in sales after an incident occurred due to the lack of a safety feature in their cars. Many customers began considering other brands of cars after this incident. How can the organization avoid losing customers
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Recalling the effected car and fixing the issue
Answer:
introducing customer retention strategies
Step-by-step explanation:
Which expression is a perfect cube?
A. -8x21y8
B. -64x64y64
C. -125x9y20
D. -216x9y18
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Expression A:
[tex] \sqrt[3]{-8x^{21}y^{8}} [/tex]
[tex] \sqrt[3]{-8} [/tex] [tex] \sqrt[3]{x^{21}[tex] \sqrt[3]{y^8} [/tex]} [/tex]
[tex]-2x^ \frac{21}{3} y^ \frac{8}{3} [/tex]
[tex]-2 x^7 y^ \frac{8}{3} [/tex]
the term [tex]y^ \frac{8}{3} [/tex] is not a perfect cube, therefore expression A is not a perfect cube.
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Expression B
[tex] \sqrt[3]{-64x^{64}y^{64}} [/tex]
[tex] \sqrt[3]{-64} \sqrt[3]{x^{64}} \sqrt[3]{y^{64}} [/tex]
[tex]-4 x^ \frac{64}{3} y^ \frac{64}{3} [/tex]
The term [tex]x^ \frac{64}{3} [/tex] and [tex]y^ \frac{64}{3} [/tex] are not perfect cube because 64/3 doesn't give whole number
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Expression C
[tex] \sqrt[3] {-125x^9y^{20}} [/tex]
[tex] \sqrt[3]{-125} \sqrt[3]{x^9} \sqrt[3] {y^{20}} [/tex]
[tex]-5 (x^ \frac{9}{3}) (y^ \frac{20}{3})[/tex]
[tex]-5 (x^3) (y^ \frac{20} {3}) [/tex]
The term [tex]y^ \frac{20}{3} [/tex] are not perfect cube because 20/3 doesn't give whole number
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Expression D
[tex] \sqrt[3]{ -216 x^{9} y^{18} } [/tex]
[tex] \sqrt[3]{-216} \sqrt[3]{x^9} \sqrt[3]{y^{18}} [/tex]
[tex]-6 ( x^ \frac{9} {3} ) ( y^ \frac{18} {3} ) [/tex]
[tex]-6 (x^3) (y^6)[/tex]
All terms are perfect cubes
ANSWER: OPTION D
does anyone know how to do this?
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such that pq=12 and p+q=b
Assuming we're looking for simple values, you can start by factorizing 12:
12 = 3*4 = 2*6 = 12*1 = -3*-4 = -2*-6 = -12*-1
For 3 and 4, b would be 7
2 and 6 => b=8
12 and 1 => b=13
and for the negatives
b can be -7, -8 or -13
So the total set is -13, -8, -7, 7, 8, 13
There are many ways to do this.
X^2+bx+12=0
[tex](-b +- \sqrt{ b^{2} -4*12 } )/2 [/tex]
This equation gives a good answer if
[tex]b ^{2} \geq 48[/tex]
Find the value of x so that the line passing through (10, 5) and (x, 9) has a slope of -2.
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(y2 - y1)/(x2-x1)
y2 = 9
y1 = 5
x2 = x
x1 = 10
So:
(9-5)/(x-10) = -2
Now, we just solve for x,
9-5 = -2(x-10)
4 = -2x+20
2x = 16
x = 8
Which postulate or theorem proves that these two triangles are congruent?
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Answer:
option B
Step-by-step explanation:
Given in the question are ∠x ≅ ∠y and ∠zwx ≅ ∠ ywz and wz is common in both.
These angles are adjacent angles of triangles.
We know theorem for congruence is Angle - Angle - Side
Therefore, for the congruence of these two triangles option B, AAS congruence theorem is the answer.
apply the distributive property and the greatest common factor to write an equivalent expression.
32k + 24 = _ (_)
what numbers should be in place of the underscores?
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Is 9.103 greater than 9.13
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Answer:
false 9.13 is greater
Step-by-step explanation:
103 thousanths are smaller then 13 hundreths
with decimals the farther you go the lower you get bc its half a number
1/2 to 1/4 to 1/8 it gets smaller
Solve x ym = y x3 for m.
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xym (1-1x2) = 0
xym (1 (un cuadrado)-1x2)=0
xym(1+x)(1-x)=0
1+x=0
1-x=0
m= 0
x=-1
x=1
Is true
m=0;x= -1;1
Find the 20th term in arithmetic sequence -4, 1, 6, 11, 16,
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What’s the ratio of 42¢ to $1.25? (Change dollars to cents)
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Answer:
42 125 becuase i got um right bozzzzzzzz
Step-by-step explanation:
What does it mean when u cant find the mean of a set of numbers?
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Answer:
Another word for mean is the "average", your goal is to find the average of the following data set, it's pretty easy, you just have to add up all the numbers in the data set and divide it with the total numbers in the data set.
For example:
Find the mean of the following data set:
4, 1, 8, 5, 7, 3
Mean: 4 + 1 + 8 + 5 + 7 + 3 = 28
then we divide 28 with 6 since there are 6 numbers in the following data set.
Mean: 4 + 1 + 8 + 5 + 7 3 = 28/6 = 4.6
We get the final answer of 4.6!
given a line whose slope is, m, is -6/5, and passes through point (-5,3), the graph will?
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y₁ = 3; x₁ = -5; m = [tex]- \frac{6}{5} [/tex]
⇒ y - 3 = [tex]- \frac{6}{5} [/tex] ( x - (-5))
⇒ y - 3 = [tex]- \frac{6}{5} [/tex] (x + 5)
Now, you can approach here in two ways: put it in the y-intercept form or the general form.
In the y-intercept form;
y - 3 = [tex]- \frac{6}{5} [/tex]x + ([tex]- \frac{6}{5} [/tex] (5))
y - 3 = [tex]- \frac{6}{5} [/tex]x - 6
y = [tex]- \frac{6}{5} [/tex]x - 3
In the general form;
y - 3 = [tex]- \frac{6}{5} [/tex] (x + 5)
by multiplying through by 5
⇒ 5 ( y - 3 ) = -6 ( x + 5)
⇒ 5y - 15 = -6x - 30
⇒ 5y + 6x = -15
∴ the line that passes through (-5, 3), with gradient [tex]- \frac{6}{5} [/tex] is
y = [tex]- \frac{6}{5} [/tex]x - 3 (y-intercept form) OR 5y + 6x = -15 (general form).
Which postulate or theorem proves that △JHG and △EFG are congruent?
SAS Congruence Postulate
ASA Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
Answers
The postulate that proves that △JHG and △EFG are congruent is;
Option B; ASA Congruence Postulate
From the given image, we can see two triangles namely;
△JHG and △EFG
Now, we can see that;
FG = GH
That is given because we see that G has divided FH into 2 equal parts.
Also, we see the right angle sign at ∠F and ∠H of both triangles.
Thus, since they are both right angles, then we can say that;
∠EFG = ∠JHG
Also, at point G, we have two vertically opposite angles which are;
∠EGF and ∠JGH
Now, from vertically opposite angle theorem, vertically opposite angles are always equal;
Thus; ∠EGF = ∠JGH
So far, we have;
FG = GH
∠EFG = ∠JHG
∠EGF = ∠JGH
This is 2 corresponding equal angles and 1 corresponding equal side. The side is included between the two angles and as such the proof that △JHG and △EFG are congruent is the ASA Congruence Postulate.
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The lenght of a rectangleis 6 inches more thans its width the area of a rectangle is 91 inches find the dimernins
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The length of a rectangular plot of land is 10 yards more than its width. If the area of the land 600 square yards , find the dimensions
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Final answer:
The dimensions of the rectangular plot of land, where the length is 10 yards more than its width and the area is 600 square yards, are 20 yards by 30 yards. We arrived at this by setting up a quadratic equation and solving for the width.
Explanation:
To find the dimensions of a rectangular plot of land where the length is 10 yards more than its width and the area is 600 square yards, we can set up an equation. Let w be the width of the plot. Then the length is w + 10 yards. The area of a rectangle is given by the formula length × width, which in our case is (w + 10) × w = 600.
Setting up the equation, we get:
w(w + 10) = 600
w^2 + 10w - 600 = 0
To solve the quadratic equation, we can factor it, use the quadratic formula, or complete the square. Factoring the equation, we find that:
(w - 20)(w + 30) = 0
Thus, the width w can be either 20 yards or -30 yards. Since a width cannot be negative, we take w = 20 yards. Then, the length is:
w + 10 = 20 + 10 = 30 yards
The dimensions of the rectangular plot of land are 20 yards by 30 yards.
64.125 - 20.37 i need the answer
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Answer:
43.755 what the other person said but I know that is the answer
Step-by-step explanation:
If 6 1/2is the lesser number in an inequality, which statement is true about the other number in the inequality?
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I KNOW ITS NOT A. But i think it is B. HOPE THIS HELPS!
If f(x)=5x^0+4x^-3 then f(a)=?
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f(a)=5(a^0)+4a^-3 a^0=1
=5(1)+4/a^3
=5+4/(a^3)
To find f(a) for the given function, substitute a for x in the function and simplify the expression.
Explanation:Given the function f(x) = 5x0 + 4x-3, we need to find f(a). To find f(a), we substitute a for x in the function. Plugging in a, we get f(a) = 5a0 + 4a-3. Since any number raised to the power of 0 is equal to 1, we have f(a) = 5(1) + 4a-3. Simplifying further, we get f(a) = 5 + 4/a3.
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Given:
AC = BC
∠3 = ∠4
Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove that triangle ACM is congruent to triangle BCM. If it is not possible to prove the triangles are congruent, choose "not possible".
Choices:
SSS
SAS
ASA
not possible
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Answer:
SAS Postulate
Step-by-step explanation:
which exponential functions have been simplified correctly check all that apply
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Answer:
Option A, C, D, are the correct options.
Step-by-step explanation:
To check the exponential functions which have been simplified correctly we will take option one by one.
A). [tex]f(x)=5(\sqrt[3]{16})^{x}=5(\sqrt[3]{2^{4}})^{x}=5(2\sqrt[3]{2})^{x}[/tex]
B). [tex]f(x)=2.3(8^{\frac{1}{2}})^{x}=2.3(2.\sqrt{2})^{x}\neq 2.3(4^{x})[/tex]
C). [tex]f(x)=81^{\frac{x}{4}}=(3^{4})^{\frac{x}{4}}=(3^{\frac{4}{4}})^{x}=3^{x}[/tex]
D). [tex]f(x)=\frac{3}{4}(\sqrt{27})^{x}=\frac{3}{4}(\sqrt{3^{3}})^{x}=\frac{3}{4}.(3\sqrt{3})^{x}[/tex]
[tex]f(x)=(24)^{\frac{1}{3}x}=(2^{3}.3)^{\frac{1}{3}x}=(2.3^{\frac{1}{3}})^{x}\neq 2(\sqrt[3]{3})^{x}[/tex]
Exponential functions and their inverses like the natural logarithm are inverse functions, meaning they can undo each other. Simplifications like ln(e^x) result in x, and e^(ln x) simplifies to x. This property is integral to correctly simplifying exponential functions.
Explanation:The exponential functions and their inverses, like the natural logarithm (ln), have specific properties where they can "undo" each other. This relationship allows us to simplify expressions involving exponentials and logarithms. For example, when you have ln(ex), this simplifies to x because the natural logarithm and the exponential function are inverse functions.
Similarly, when applying the exponential function to a natural logarithm, like eln(x), the result is just x. Furthermore, when taking square roots of exponentials, you can adjust the exponent to be evenly divisible by 2 and then take the square root of the base number, followed by dividing the exponent by 2. Also, while dividing exponentials, you subtract the exponents when the bases are the same.
Here is an example of this simplification: to compute the square root of e4, we can write it as e4/2, which simplifies to e2.
Which ordered pair comes from the table ? HELPPP!
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Write the polynomial in factored form. 4x3 + 8x2 – 96x
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Explanation:
4x^3, 8x^2 and 96x have 4x as a common factor. Hence
4x^3+8x^2-96x = 4x*(x^2+2x-24)
Furthermore, (x^2+2x-24)= (x-4)(x+6)
because 6-4=2 and 6*(-4) = -24.
So 4x^3+8x^2-96x = 4x*(x^2+2x-24) = 4x(x-4)(x+6).
PLZ HELP ILL GIVE A BRAINLIEST SHOW ALL WORK!!!!
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(√3 + 2√3) + √7
Step 2. Simplify
3√3 + √7
That's all.
What is the measure of x?
A.36
B.72
C.144
D.360
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Mrs. simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer.
a. write and solve an equation to find the integers.
b. does the equation have one solution, no solutions, or is it an identity? explain.
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Final answer:
To find two consecutive even integers, we can set up and solve an equation. The equation in this case is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions.
Explanation:
To find two consecutive even integers, let's represent the first integer as x and the second integer as x + 2. Now, according to the given information, twice the lesser of the two integers is 4 less than two times the greater integer. We can write this as:
2x = 2(x + 2) - 4
Simplifying the equation:
2x = 2x + 4 - 4
2x = 2x
This equation is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions. In this case, there are infinitely many pairs of consecutive even integers that satisfy the given conditions.
Please help! I need to show my work
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Notice that sides AB and CD are horizontal, so they are parallel with different lengths.
Sides BC and Ad are not parallel.
A quadrilateral with two parallel sides and two non-parallel sides is a trapezoid.
Find three consecutive odd integers whose sum is negative 465
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465 / 3 = 155
so -153 + -155 + -157 = -465