Answer:
a=2
Step-by-step explanation:
Given: 5a-12=-2
Isolate Variable: 5a=10
Divide: a=2
Answer:
5a - 12= -2
5 x 2= 10 so,
5(2) - 12= -2
^
10-12= -2
Use the drawing tools to form the correct answers on the graph. Plot the zeros of this function: f(x) = (x – 1)(x – 7).
The answer is in the graph picture
The zeros of the function f(x) = (x - 1)(x - 7) are 1 and 7
The function is given as:
f(x) = (x - 1)(x - 7)
Set the function to 0.
So, we have:
f(x) = (x - 1)(x - 7) = 0
This gives
(x - 1)(x - 7) = 0
Split
(x - 1) = 0 or (x - 7) = 0
Remove brackets
x - 1 = 0 or x - 7 = 0
Solve for x
x = 1 or x = 7
Hence, the zeros of the function are 1 and 7
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1. There were 88 birds in the tree and then b of the birds flew away. Write an expression that shows how many birds are in the tree now.
2. Brice had $73 and then he earned d more dollars. Write an expression that shows how much money he has now.
3. Kurt's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
can you graph 6=6? infinite solutions
Answer:6 = 6 represents a true statement because 6 is always equal to 6. When graphed on a coordinate plane, this equation would result in a straight line at y = 6, which means that every point on the line corresponds to a solution of the equation. Since the line extends infinitely in both directions, there are infinitely many solutions to this equation.
Step-by-step explanation:
What is the slope of the line containing the points (3,4) and (-6,10)
Answer:-.6666666667x +6
Step-by-step explanation:
I have a school calculator
Answer:
-2/3 is the slope
Step-by-step explanation:
Slope = y2 - y1/x2 - x1
= 10 - 4/-6 - 3
= 6/-9
=-2/3
use the fact that 2 1/2 divided by 1/8 equals 20 to find 2 1/2 divided by 5/8.
Answer:
The value of the expression is 4.
Step-by-step explanation:
Consider the provided information.
We have given that:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]
Now we need to find the value of:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =?[/tex]
Consider the provided fact:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]
Multiply [tex]\frac{1}{5}[/tex] both sides.
[tex]\dfrac{1}{5}\times \dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]
[tex]\dfrac{1\times2\dfrac{1}{2} }{5\times\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =4[/tex]
Hence, the value of the expression is 4.
How many groups of 14 are in 28?
Answer:
there are 2 groups
Step-by-step explanation: 14 x 2 = 28
4 times a number divided by 3 is 5 more than that number divided by 2 what is the value of that number
Answer:
x=6
Step-by-step explanation:
Let the number be x
Then 4 times a number divided by 3 is 5 more than that number divided by 2 gives the equation:
[tex] \frac{4x}{3} = \frac{x}{2} + 5[/tex]
Multiply through by the LCD, which is 6.
[tex] 6 \times \frac{4x}{3} = 6 \times \frac{x}{2} + 5 \times 6[/tex]
Cancel out to obtain:
[tex] 2 \times 4x =3 \times x + 30[/tex]
[tex]8x = 3x + 30[/tex]
Group similar terms
[tex]8x - 3x = 30[/tex]
Simplify the LHS
[tex]5x = 30[/tex]
Divide both sides by 5 to get:
[tex]x = 6[/tex]
Multiply.
(x-6)(5x-4)
O
A. 5x^2-30x + 24
B. 5x^2 - 34x + 24
c. 5x^2 - 26x-24
D. 5x^2 - 30x-24
A triangle with the coordinates (6,4), (2,-1), and (-3,5) is translated 4 Units left and rotate 180 degrees about the origin. What are the coordinates of the image.
Answer:
(-2,-4),(2,1), and (7,-5)
Step-by-step explanation:
The given triangle has coordinates (6,4), (2,-1), and (-3,5).
When we translate 4 units left, the we obtain:
(6,4)------>(6-4,4)=(2,4)
(2,-1)----->(2-4,-1)=(-2,-1)
(-3,5)----->(-3-4,5)=(-7,5)
When the resulting figure is rotated 180° about the origin, the coordinates of the final figure becomes
(2,4)------>(-2,-4)
(-2,-1)----->(2,1)
(-7,5)------->(7,-5)
NB: The mapping for 180° rotation is:
(x,y)----->(-x,-y)
after 2/5 of the kittens were given away, there was k kittens and p puppies left in the pet store. write and algebraic expression in terms of k
Answer:
Algebraic expression in terms of k
k= T- p
Step-by-step explanation:
As
no of kittens left = k
no of puppies left =p
If total left after giving away kittens =T
T = p + k
In terms of k the expression will be
k= T- p
Keywords: Algebra
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Final answer:
To write an algebraic expression in terms of k, subtract the number of kittens given away from the initial number of kittens. The algebraic expression in terms of k is (3/5)x.
Explanation:
To write an algebraic expression in terms of k, we need to determine the initial number of kittens before any were given away. Let's call this number 'x'. According to the problem, 2/5 of the kittens were given away. This means that (2/5)x kittens were given away, leaving k kittens remaining.
To find the algebraic expression in terms of k, we subtract the number of kittens given away from the initial number of kittens. So the expression is x - (2/5)x = k.
We can simplify this expression by finding a common denominator for the fractions. In this case, the common denominator is 5. So the expression becomes 5x/5 - (2/5)x = k. Simplifying further, we have (3/5)x = k. Therefore, the algebraic expression in terms of k is (3/5)x.
What is the prime factorization of 40?
2 times 5
2 times 20
2 times 2 times 2 times 5
2 times 2 times 4 times 5
Answer:
C.
Step-by-step explanation:
2 times 2 times 2 times 5 = 40
The prime factorization of 40 is 2 times 2 times 2 times 5, which can be written as 2^3 * 5. So, option C, "2 times 2 times 2 times 5," is the correct prime factorization of 40.
The prime factorization of the number 40 is 2^3 * 5. To arrive at this factorization, we break down 40 into its prime factors. We start by dividing 40 by the smallest prime number, 2. Since 40 is even, it can be divided by 2 evenly, resulting in 20. We continue this process until we can no longer divide by 2, which leaves us with 20. Now, we try to divide 20 by the next smallest prime, which is also 2. This division gives us 10. Once again, we divide by 2, and we are left with 5. Since 5 is a prime number, we cannot further divide it. Therefore, we have prime factorized 40 as 2 * 2 * 2 * 5, which can be expressed as 2^3 * 5, where the exponent 3 indicates that we have three 2s multiplied together, and the 5 is the prime factor on its own.
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Which expression simplifies...
Answer:
see below
Step-by-step explanation:
If suffices to look at the last term. It must simplify to 4/(3w²), so the exponents of z must match in numerator and denominator, and the ratio of constants must reduce to 4/3.
The exponents of z have the right values in choices B and D, but the ratio of constants only matches in choice D. Looking at the rest of choice D, we see that we can factor 6w²z² from both numerator and denominator, then factor 2 from the remaining numerator to make it match the desired form.
[tex]\dfrac{(12w^2z^4-24w^2z^2)}{18w^4z^2}=\dfrac{6w^2z^2}{6w^2z^2}\cdot\dfrac{2z^2-4}{3w^2}=\dfrac{2(z^2-2)}{3w^2}[/tex]
How to do similar polygons?
Answer:
Similar polygon
Step-by-step explanation:
If two polygon similar then the ratio of the corresponding sides is the scale factor.All interior angles are congruent.Translate the following sentence into an equation. The sum of twice a number x and 13 is two less than three times x.
Question 20 options:
a)
2x + 13 = 3x – 2
b)
2(x + 13) + 3x – 2
c)
2x + 13 = 2 – 3x
d)
2x + 13 = 3(x – 2)
Answer:
2x + 13 = 3x - 2
Step-by-step explanation:
This should be the answer
Answer:
its 2
Step-by-step explanation:
Sarai is mixing a solution. She pours all the liquid from a full small beaker into a larger beaker. The liquid fills the large beaker to 15% of its capacity. If the small beaker holds 300 mL, how much does the large beaker hold?
Answer:
2000 ml
Step-by-step explanation:
Given: Sarai pours all the liquid from a full small beaker into a larger beaker.
The liquid fills the large beaker to 15% of its capacity.
The small beaker holds 300 ml.
Lets assume capacity of large beaker to hold be "x".
As given, Sarai pours all the liquid from a full small beaker into a larger beaker
∴ [tex]15\% \times x= 300\ ml[/tex]
⇒ [tex]0.15x= 300[/tex]
Dividing both side by 0.15
⇒[tex]x= \frac{300}{0.15}[/tex]
∴ [tex]x= 2000\ ml[/tex]
Hence, the large beaker can hold 2000 ml of liquid.
Carter plays 5/8 of a basket ball game. The basket ball game is 40 minutes long. Which if the following shows how to find the number of minutes carter plays?
Answer:
25 minutes is how long Carter played
Step-by-step explanation:
To find out how many minutes Carter plays, multiply 40 minutes by 5/8, which results in 25 minutes of playtime.
Explanation:Finding the Number of Minutes Carter PlaysTo determine the number of minutes Carter plays in a basketball game, which is 40 minutes long, when he plays 5/8 of the game, we use multiplication. We multiply the total game time by the fraction of the game played:
40 minutes (total game length) × (5/8) (fraction of the game played)Steps to calculate:
Multiply the numerator of the fraction (5) by the total game time (40 minutes). 5 × 40 = 200.Divide the product by the denominator of the fraction (8). 200 ÷ 8 = 25 minutes.Therefore, Carter plays for 25 minutes of the basketball game.
5) Find the equation of a line in slope-intercept form through the point
(3,-4) and perpendicular to the line x + y = 4.
Answer:
y = -x + 4
perp: m = 1
y + 4 = x - 3
y = x - 7
Step-by-step explanation:
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Explain when you must write the number 1, and when you do not need to.
Answer:
The number 1 is not necessary when expressing powers of one. For example, you needn't write "5" as [tex]5^{1}[/tex].
Step-by-step explanation:
The number 1 is written when it is part of a larger number, as it is significant. It is not necessary to write leading zeros. In scientific notation, trailing zeros are excluded, and the number is written in a form where only non-zero digits appear before the decimal.
Explanation:Understanding when to write the number 1 and when it's not needed depends on the context in mathematics, especially when dealing with significant figures and scientific notation. Generally, all non-zero numbers are considered significant (rule 1), which means that when a value like 1 is part of a larger number, it contributes to the meaning of that number. However, leading zeros do not count as significant (rule 3).
In the case of multiplication by units, like converting from kilograms to grams, we utilize the concept of multiplying by the number 1 to affect the units without changing the value. For example 0.7 kg can be multiplied by 1000/1 (1000 g / 1 kg) to convert to grams. This is because 1000/1 is equal to 1000, indicating multiplication by one does not change the value.
When expressing numbers in scientific notation, it's important to include the non-zero digits only before the decimal point, excluding any trailing zeros. Thus, 1,500,000 would be written as 1.5 x 106, with the power indicating the necessary number of decimal point movements to place it after the first significant digit.
Financing a balloon payment under a new fixed rate loan is called a
A reset option
O
B. loan adjustment
O
c. balloon refinance
D. exercise option
Answer:
rest set option
Step-by-step explanation:
The graph of which function has a minimum located at (4, –3)?
f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35
Answer:
f(x) = 1/2x^2 – 4x + 5 (the third option)
Step-by-step explanation:
I looked it up on a graphing calculator.
The quadratic function that has a minimum located at (4, -3) is:
[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]
Which function has a minimum located at (4, -3)?All the options are quadratic functions, so we need to find the one with a leading coefficient positive, which also has a vertex at (4, -3).
The 3 ones with positive leading coefficients are:
[tex]f(x) = (1/2)*x^2 + 4x -11[/tex]
[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]
[tex]f(x) = 2x^2 - 16x + 35[/tex]
The vertex of the first one is at:
[tex]x = -4/(2*1/2) = -4[/tex]
The x-value of the vertex must be x = 4, so we can discard this.
For the second quadratic function the x-value of the vertex is:
[tex]x = -(-4)/(2*1/2) = 4[/tex]
Then the y-value of the vertex is:
[tex]f(4) = (1/2)*4^2 - 4*4 + 5 = -3[/tex]
Then the vertex is at (4, -3), so this is the correct option.
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If you need 100 trucks for every 1500 yards, how many will you need for 1000 yards ?
Kevin has an after-school delivering advertising after 9 weeks he had earned a mean of $24 per week how much does he need to earn in the 10th week to increase his mean weekly earnings to $25
Answer:
$34
Step-by-step explanation:
So he earns $24 per week (ima just say p/w to make it shorter) meaning he earned around $216 in total. To get to $25 p/w, you have to get $250 in total from the 10 weeks. So $250 - $216 = $34.
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Good morning,
which of the following rational functions is graphed below? thanks
Answer:
C.x/(x+5)(x-2)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Write the Equation of the line in slope intercept form
(0, -3), (7.5,0)
Answer:
Step-by-step explanation:
First, start off by solving for the slope using this formula:
[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Then, plug in the values: [tex]\frac{0-(-3)}{7.5-0}[/tex]
Solve the equation: [tex]\frac{3}{7.5}[/tex]
That's your slope.
Then plug in one of the coordinates given in the problem for x and y and solve this equation:
y=[tex]\frac{3}{7.5}[/tex]x+b
Hope that helped!!! :)
Someone help me with this please. I can’t figure It out.
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles add up to 90 degrees
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x minus 2, y + 2), what will be the coordinates of A prime?
Answer:
A' (-4,0)
Step-by-step explanation:
The complete question is
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x minus 2, y + 2), what will be the coordinates of A prime? On a coordinate plane, triangle A B C has points A(negative 2, negative 2), B(negative 2, negative 4), C(2, negative 4)
we know that
The rule of the translation is
(x,y) -----> (x-2,y+2)
The coordinates of point A (-2,-2)
Applying the rule of the translation to coordinate A
A (-2,-2) ----- A' (-2-2,-2+2)
A (-2,-2) ----- A' (-4,0)
Answer:
The answer is A on edge
Step-by-step explanation:
2. Graph each equation using a table of values.
(a)) y = 3x - 1
Make an x and y table, and pick any values to plug in for x in the equation.
I will use the numbers from -2 to 2
Now plug in the values you picked for x into the equation to find its y-value
x = -2
y = 3x - 1 Plug in -2 for x
y = 3(-2) - 1
y = -6 - 1
y = -7
x = -1
y = 3x - 1
y = 3(-1) - 1
y = -3 - 1
y = -4
Do the same for the rest of the numbers, and graph each point and draw a line connecting them.
A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 4 divided by ft for the legs and $ 16 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.
Answer:
[tex]\frac{8h}{\sqrt{2}} + 16h[/tex]
Step-by-step explanation:
First we need to compute the side length as a function of h
So x be the side length of the right isosceles triangle, in Pythagorean formula we have
[tex]x^2 + x^2 = h^2[/tex]
[tex]2x^2 = h^2[/tex]
[tex]x = \frac{h}{\sqrt{2}}[/tex]
The cost for the legs is
[tex]C_l = 4*2x = \frac{8h}{\sqrt{2}}[/tex]
The cost for the hypotenuse is
[tex]C_h = 16h[/tex]
So the total cost in term of h is
[tex]C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h[/tex]
The total cost C of construction as a function of h is C = 16 / h + 8√2 / h
The pen is in the shape of an isosceles right angle. This means one of the
angle is 90 degrees and 2 sides of the triangle are equal and the base angles
are equal too.
Using pythagora's theorem
Therefore,
x² + x² = h²
2x² = h²
x² = h² / 2
x = √h²/ √2 = h/√2
cost of the legs = 4 / h/√2 + 4 / h /√2 = 8√2 / h
cost of the hypotenuse = 16 / h
Total cost = 16 / h + 8√2 / h
C = 16 / h + 8√2 / h
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Which is the value of this expression when a = 5 and k = negative 2? (3^2 a^-3)(3 a^-4)^-2
Answer: C 25/9
Step-by-step explanation: