Consecutive numbers means numbers one after another. 1 and 2 are consecutive numbers
The answer would be 18 and 19
18 + 19 is 37
Hope this helped!
~Just a girl in love with Shawn Mendes
Jill picks a number at random and multiplies it by 2 and adds five to the product. She then multiplies the sum by -3 and subtracts 7 from the product. After these four steps her new number is -40. What was her original number?
Answer:
3
Step-by-step explanation:
Say Jill picks the number x.
She multiplies it by 2 giving 2x.
It says add 5 to that product giving 2x+5.
She multiplies this sum by -3 giving -3(2x+5).
She then subtracts 7 from that product giving -3(2x+5)-7.
Her number after doing all of this is -40 so we hae -3(2x+5)-7=-40
To solve:
First: I would add 7 on both sides: -3(2x+5)=-33
Second: I would divide boht sides by -3: 2x+5=11
Third: I would subtract 5 on both sides: 2x=6
Last: I would divide both sides by 2: x=3
which of the following statements is always true about the function y=a•b^x
Answer:
c. When a > 0 and b > 1, the function models exponential growth.
Step-by-step explanation:
You have exponential decay when a > 0 and 0 < b < 1.
The statement that is always true about the function y=a•b^xc is this: C. When a > 0 and b > 1, the function models exponential growth.
What is an exponential growth?Exponential growth is a type of growth that occurs as there is an addition of numbers. This is reflected in the upward movement of the graph if such growth is represented in a graph.
So, the statement that best reflects this meaning of exponential growth is that when in a function, a > 0 and b > 1, then exponential growth is modeled. Thus, the correct option number is C. "When a > 0 and b > 1, the function models exponential growth."
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ABC is dilated by a scale factor of 3 with the origin as the center of dilation, resulting in the image A'B'C'. If the slope of line AB is -1.2, what is the slope of line A'B'?
A. -1.2
B. 3.6
C. 1.2
D 1.8
Answer:
The slope of A'B' = -1.2 ⇒ answer A
Step-by-step explanation:
* Lets talk about dilation
- A dilation is a transformation that changes the size of a figure.
- It can become larger or smaller, but the shape of the
figure does not change.
- The scale factor, measures how much larger or smaller
the image will be
- If the scale factor greater than 1, then the image will be larger
- If the scale factor between 0 and 1, then the image will be smaller
- If the center of the dilation is the origin then multiply each coordinate
by the scale factor
* In the problem
∵ Δ ABC is dilated by a scale factor of 3 with the origin as the center
of dilation
- Let point A is (a , b) and point B is (c , d)
∵ The slope of the line which passes through points (x1 , y1) and (x2 , y2)
is m = (y2 - y1)/(x2 - x1)
∴ The slope of AB = (d - b)/(c - a) = -1.2
∵ Point A' is (3a , 3b) and point B' is (3c , 3d)
∴ The slope of A'B' = (3d - 3b)/(3c - 3a)
- Take 3 as a common factor from up and down
∴ The slope of A'B' = 3(d - b)/3(c - a) ⇒ cancel 3 up with 3 down
∴ The slope of A'B' = (d - b)/(c - a) = the slope of AB
∵ The slope of AB = -1.2
∴ The slope of A'B' = -1.2
* The slope of A'B' = -1.2
midpoint of the line segment (-1,5) (-8,-4)
Answer:
(- [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )
Step-by-step explanation:
Using the midpoint formula
Given 2 points (x₁, y₁ ) and (x₂, y₂ ), then midpoint is
([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex])
with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (- 8, - 4), then midpoint
= ([tex]\frac{-1-8}{2}[/tex], [tex]\frac{5-4}{2}[/tex] )
= ( - [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )
Answer:-4.5,0.5
Step-by-step explanation:midpoint =x1+x2/2, y1+y2/2
-1+-8/2=x,-4+5/2=y
-9/2=x,1/2=y
-4.5=x, 0.5=y
Fixed rate mortgage offer:
Purchase price: $170,000
Down payment ($34K): 20%
Term: 30 years
Interest rate: 4.25%
Property tax (yearly): $1,500
Homeowner’s insurance (yearly): $1,000
Use this example from a fixed-rate mortgage calculator to help you answer the questions. Keep the page open after you complete this question.
According to the calculator, the monthly payment Demarco and Tanya should anticipate paying for principal and interest is
$208.
$877.
$669.
$1,200.
Answer: its C. $669
Step-by-step explanation:
X^2 +x-6=0
How to solve this ?
Answer:
x = 2, x = -3
Step-by-step explanation:
We are given the following quadratic equation and we are to solve it for x:
[tex] x ^ 2 + x - 6 = 0 [/tex]
We need to find such factors of -6 that when added give a result of 1 and when multiplied, give a product of -6.
[tex] x ^ 2 + x - 6 = 0 [/tex]
[tex] x ^ 2 - 2x + 3x - 6 = 0 [/tex]
[tex] x ( x - 2 ) + 3 ( x - 2 ) = 0 [/tex]
[tex](x-2) = 0, (x+3)=0[/tex]
x = 2, x = -3
ABCD is a parallelogram. What are the measures of angles B and C? b=(3n+20) D= (6n-25)
Answer:
B = 65
C = 115
Step-by-step explanation:
Givens
ABCD is a parallelogram
It is lettered in such a way that B is opposite D
B = 3n+20
D = 6n-25
Solution
<B = <D Property of Parallelogram
3n + 20 = 6n - 25 Add 25 to both sides
3n + 20 + 25 = 6n Combine
3n +45 = 6n Subtract 3n from both sides
3n +45 = 6n-3n Combine
45 = 3n Divide by 3
45/3=3n/3
n = 15 Value of n
B = 3n + 20 Find B. Let n = 15
B= 3*15+20 Combine
B = 45 + 20 Combine
B = 65
==================
B and C are supplementary. They add up to 180
B + C = 180
65 + C = 180
C = 180-65
C = 115
What is the y-value in the solution to this system of linear equations?
4x + 5y = −12
-2x + 3y = −16
A.)−4
B.)−2
c.)2
D.)5
Answer:
Option A.)−4
Step-by-step explanation:
we have
4x+5y=-12 -----> equation A
-2x+3y=-16 -----> equation B
Solve the system of equations by elimination
Multiply the equation B by 2
2*(-2x+3y)=-16*2
-4x+6y=-32 -----> equation C
Adds equation A and equation C
4x+5y=-12
-4x+6y=-32
-----------------
5y+6y=-12-32
11y=-44
y=-4
Answer with Step-by-step explanation:
We are given a system of linear equations:
4x + 5y = −12
-2x + 3y = −16
Multiply second equation by 2 and add it to first equation.
4x+5y-4x+6y= -12-32
⇒ 11y= -44
Dividing both sides by 11
⇒ y= -4
Hence, the y-value in the solution to the system of linear equations
4x + 5y = −12
-2x + 3y = −16 is:
A.)−4
Rewrite the following radical expression in rational exponent form.
[tex]( \sqrt{x)} ^5[/tex]
Answer:
Step-by-step explanation:
note that the square root of any number can be expressed as the number raised to a [tex]\frac{1}{2}[/tex] power
i.e √a = [tex]a^{\frac{1}{2} }[/tex]
Applying this to our expression
[tex](\sqrt{x} )^{5}[/tex]
= [tex]x^{\frac{1}{2} * 5 }[/tex]
= [tex]x^{\frac{5}{2}}[/tex]
The Answer Is...
x^5/2
[tex]x^ \frac{5}{2}[/tex]
In a class of 32 students, the mean height of the 14 boys is 1.56 metres. The mean height of all 32 students is 1.515 metres.
Work out the mean height of the girls.
Answer:
1.48 m
Step-by-step explanation:
mean height of 14 boys is 1.56 m, so their total height is 14 * 1.56 = 21.84 m
mean height of 32 students is 1.515 m, so their total height is 48.48
48.48 - 21.84 = 26.64 (total height of the girls)
mean height of the girls is 26.64/18 = 1.48 m
Answer:
1.48 m.
Step-by-step explanation:
There are 32 - 14 = 18 girls in the class.
Total height of the whole class = 1.515 * 32
= 48.48 m..
Total height of all the boys = 14 * 1.56 = 21.84 m.
So the total height of the 18 girls = 48.48 - 21.84
= 26.64 m.
Therefore the mean height of the girls
= 26.64 / 18
= 1.48 m.
Which of the following symbols make(s) the following mathematical statement true? Select all that apply. 49 ___ 3 + 32 ÷ 23
49 ___ 3 + 32 ÷ 23
49 ___ 3 + 1.39
49 ___ 4.39
49 > 4.39 is the only possible answer. 49 is greater than 4.39.
To determine the correct symbol for the expression 49 ___ 3 + 32 ÷ 23, first calculate the right side following PEMDAS, resulting in 7. Then compare it with the left side (49), which shows that 49 is greater than 7, so the correct symbol is '>'.
Explanation:The question asks which symbol makes the mathematical statement true for the expression 49 ___ 3 + 32 ÷ 23. We need to solve the right side of the equation first before we can determine the correct symbol to use.
To solve 3 + 32 ÷ 23, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division as they appear from left to right, Addition and Subtraction as they appear from left to right). First, we solve the exponent 23, which equals 8. Then, we perform the division: 32 ÷ 8 = 4. Finally, we add 3 to the result: 3 + 4 = 7. So, our expression on the right side of the equation is equal to 7.
Now we compare the left side of the equation (49) with the result we calculated (7). It is evident that 49 is greater than 7, so the correct symbol to use would be '>'. Therefore, the complete and true mathematical statement would be: 49 > 3 + 32 ÷ 23 or 49 > 7.
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Prove the following
(cot0+cosec0)
[tex](cot0 + cosec0) { }^{2} = \frac{1 + cos0}{1 - cos0} [/tex]
[tex]\bf [cot(\theta )+csc(\theta )]^2=\cfrac{1+cos(\theta )}{1-cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand side}}{[cot(\theta )+csc(\theta )]^2}\implies cot^2(\theta )+2cot(\theta )csc(\theta )+csc^2(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+2\cdot \cfrac{cos(\theta )}{sin(\theta )}\cdot \cfrac{1}{sin(\theta )}+\cfrac{1}{sin^2(\theta )}\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{2cos(\theta )}{sin^2(\theta )}+\cfrac{1}{sin^2(\theta )}[/tex]
[tex]\bf \cfrac{\stackrel{\textit{perfect square trinomial}}{cos^2(\theta )+2cos(\theta )+1}}{sin^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the right-hand-side}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}}\implies \stackrel{\textit{multiplying by the denominator's conjugate}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}\cdot \cfrac{1+cos(\theta )}{1+cos(\theta )}}[/tex]
[tex]\bf \cfrac{[1+cos(\theta )]^2}{\underset{\textit{difference of squares}}{[1-cos(\theta )][1+cos(\theta )]}}\implies \cfrac{[cos(\theta )+1]^2}{1^2-cos^2(\theta )} \\\\\\ \cfrac{[cos(\theta )+1]^2}{1-cos^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}}[/tex]
recall that sin²(θ) + cos²(θ) = 1, thus sin²(θ) = 1 - cos²(θ).
What is the converse of the following true conditional? If the converse is true, rewrite the statements as a biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
Select one:
a. If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
b. If two lines do not intersect, they are parallel. One statement is false. If two lines are parallel, they may intersect twice.
c. If two lines do not intersect, they are parallel. Both statements are true. Two lines are parallel if (and only if) they do not intersect.
d. If two lines do not intersect, they are not parallel. Both statements are true. Two lines are not parallel if (and only if) they do not intersect.
Answer: A
Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:
Conditional: If someone like ice cream, they have brown hair
Converse: If someone has brown hair, they like ice cream
The converse of our given conditional would be:
If two lines do not intersect, they are parallel
This eliminates Option D
Next, the converse is false.
Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they could be either parallel or skew.
This eliminates Option C and B, leaving us with Option A
We want to find the converse statement to one given statement and see if it is true.
We will see that the correct option is a:
If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
A general statement is written as:
If P then Q.
Where P and Q are two given propositions.
The converse statement to the above shown is:
If Q then P.
For this question, we have the statement:
If two line are parallel, they do not intersect.
Then we can write the converse statement as:
If two lines do not intersect, they are parallel.
Which is false, in 3-dimensions we can have two non-parallel lines that don't intersect each other (parallel lines must not intersect and also live on the same plane).
Then the correct option is the first one:
a: If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.
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Robin and Jim took cherries from a basket . Robin took 1/4 of the cherries and Jim took 1/8 of the cherries. What fraction of the cherries did they took altogether?
Can you please help me and I will get you Brainliest.
Answer:
3/8
Step-by-step explanation:
We must first find the LCD in order to add up the amounts taken from the basket.
The Least Common Denominator of 4 and 8 is 8.
We convert 1/4 so that it is a fraction over 8, which is 2/8
2/8+1/8=3/8
Answer:
3/8
Step-by-step explanation:
We want to find the total amount of cherries that Robin and Jim took
1/4 + 1/8
The common denominator is 8
1/4 *2/2 = 2/8
Replacing 1/4 with 2/8
2/8 + 1/8 = 3/8
The fraction that they took is 3/8
What is the product?
(2x – 1)(х + 4)
О2x? – 4
О 2х2 + 4
ОООО
02x2 +7x – 4
2х2 -7x - 4
EMERGENCY!! 30 POINTS!!
Jasmine and Carlotta are sisters, and each have their own savings. Tog
movies. Each girl has to pay back an equal amount Carlotta also owes
change in Carlotta's savings after she repays her brother?
A. -28= 2 + (-6)
B. 28- 2 + (-6)
C. -28 2+(-6)
D. -28 = 2-(-6)
You would need to divide the money by 2 ( both sisters) to get the equal amount they each need to pay. Then include the extra amount Carlotta owes.
The correct equation would be -28 ÷ 2- (-6)
Answer:
a
Step-by-step explanation:
The tiles on the left contain functions written using function notations. Match each function with its input
Answer:
Part 1) h(g)=-4+g ----> the input is g
Part 2) f(h)=-h-7 -----> the input is h
Part 3) g(f)=-2f -----> the input is f
Step-by-step explanation:
Part 1) we have
h(g)=-4+g
we know that
The input is the independent variable and the output is the dependent variable
so
the output is h(g) or 4+g
the input is the variable g
Part 2) we have
f(h)=-h-7
we know that
The input is the independent variable and the output is the dependent variable
so
the output is f(h) or h-7
the input is the variable h
Part 3) we have
g(f)=-2f
we know that
The input is the independent variable and the output is the dependent variable
so
the output is g(f) or 2f
the input is the variable f
Answer: Questions are in different places than other people screen.
h(g) = -4+g - The input is G
g(f) = 2f - The input is F
f(h) = h - 7 - The input is H
Step-by-step explanation:
Just put tha answer in nd get a good grade :)
An orange traffic cone has a diameter of 10 in. and a height of 28 in.
What is the volume of the cone?
Use 3.14 for
π
.
Enter your answer in the box as a decimal to the nearest cubic inch.
Answer:
733 inches
Step-by-step explanation:
V= 3.14*5^2*28/3
Order of Operations (PEMDAS)
5^2=25
25*3.14= 78.5
78.5*28= 2198
2198/3=732.66
Round to nearest cubic inch
733 inches
Which of the following is NOT a possible value of the correlation coefficient?
A. negative 0.9
B. zero
C. positive 0.15
D. positive 1.5
E. negative .05
Answer:
positive 1.5
Step-by-step explanation:
by definition, the possible values for correlation coefficients are
-1 ≤ correlation coefficient ≤ 1
+1.5 lies outside this range and hence is not valid.
The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to +1. Therefore, a value of positive 1.5, as listed in option D, is not a possible value for a correlation coefficient.
Explanation:In mathematics, particularly in statistics, a correlation coefficient is a measure of the strength and direction of the linear relationship between two variables on a scatterplot. The value of a correlation coefficient ranges from -1 to +1. A correlation coefficient of +1 indicates a perfect positive linear relationship, a correlation coefficient of -1 indicates a perfect negative linear relationship, and a correlation coefficient of 0 indicates no linear relationship.
Therefore, the answer to the question is: D. positive 1.5. This is not a possible value for a correlation coefficient because it lies outside the acceptable range of -1 to +1.
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Consider the following quadratic equation. Determine a possible value of b so that the quadratic has two complex solutions. -14 12 -16 14
Answer:
Can you attach the quadratic equation?
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
PLATO user
Kyra and her twin sister share shoes. In there closet they have four pairs of Sandals,five pairs of tennis shoes, and three pairs of boots. What is the probability that kyra selects a pair of sandals, put them on and then her sister selects a pair of tennis shoes?
Answer:
Step-by-step explanation:
The total number of shoes they share is
4 + 5 + 3 = 12
Kyra: 4/12 = 0.333333
Tennis Shoes: There are now 11 shoes. 5/11 = 0.46
The probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes is 3/20.
Explanation:To find the probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes, we need to determine the total number of possible outcomes and the number of favorable outcomes.
There are 4 pairs of sandals, 5 pairs of tennis shoes, and 3 pairs of boots in the closet. Assuming Kyra selects a pair of sandals first, she has 4 options. After Kyra selects the sandals, there will be 3 pairs of sandals left.
Since the sandals are chosen without replacement, her sister will have 5 options for the pair of tennis shoes. The total number of possible outcomes is the product of the options for each step: 4 * 5 = 20.
Therefore, the probability that Kyra selects a pair of sandals and her sister selects a pair of tennis shoes is 3/20.
70 Points!! Question!
Answer:
409.86
Step-by-step explanation:
First find the mark up
230 *65%
230 * .65 = 149.50
The new cost of the tent is the original cost plus the mark up
230 + 149.50
379.50
Now we need to find the tax
379.50 * 8%
379.50 *.08
30.36
The total cost is the cost of the tent plus the tax
379.50 + 30.36
409.86
Answer:
409.86
is the correct answe rfor this question
I need help with PLATO Course Texas Algebra II, Semester A do you think you can help me with the answers?
Find the lateral area for the cylinder with the given measurement
r= 4, h= 5
20 Pi square units
40 Pi square units
80 Pi square units
[tex]\bf \textit{lateral area of a cylinder}\\\\ LA=2\pi rh~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=5 \end{cases}\implies LA=2\pi (4)(5)\implies V=40\pi[/tex]
Evaluate
[32+ (7.6 - 22)] - [30 = (4 + 1)]
Answer:
I got 11.6
Step-by-step explanation:
Hope my answer has helped you in any way!
Which graph represents the function p(x) = |x – 1|?
Answer:
The last one
Step-by-step explanation:
Your equation is p(x) = |x - 1|
The function equation can be represented by f(x) = a|x - h| + k
To find the vertex, you have to find (h,k)
In the equation p(x) = |x - 1|, 1 is h [since its (+h,k) not (-h,k)]
k is 0 since there is no +k after |x-1|.
So, your vertex will be at (1,0)
Thus, the answer is the last graph.
[I also graphed it on a graphing calculator so you can check. :) ]
The vertex will be at (1, 0).
Functions of graphs
The given equation is p(x) = |x - 1|
The function equation can be defined by f(x) = a|x - h| + k
To calculate the vertex, you have to identify (h, k)
In the given equation p(x) = |x - 1|, 1 exists h
[since its (+h, k) not (-h, k)]
k exists 0 since there does not exist +k after |x-1|.
So, the vertex will be at (1, 0).
Therefore, the graph represents the function p(x) = |x – 1| is option (d).
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what is the rang for the equation y=2x-3
Answer:
The range for the equation is all real numbers.
Step-by-step explanation:
The range of an equation is the set of y-values that you can get by plugging in all possible x-values.
Another way to put it is, when you graph the equation, whatever y-values the line produces, is its range.
Graphing y=2x-3, you can see it is a graph with a positive slope that extends from negative infinity y-value to positive infinity x-value.
Mathieu is finding the x-intercepts of the function f(x) = x2 + 4x + 3. His work is shown below
. Which error did Mathieu make?
Answer:
I can't see Mathieu's work but I will show the right steps and maybe you can find where Mathieu went wrong.
f(x)=x^2+4x+3
f(x)=(x+3)(x+1) Since 3*1=3 and 3+1=4
The x-intercepts can be found by setting y to 0 and solving for x
(in other words replace that f(x) thing with 0 and solve for x)
0=(x+3)(x+1)
Now set both factors equal to 0
x+3=0 or x+1=0
x =-3 x=-1
The x-intercepts are at (-3,0) and (-1,0)
A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The x-intercepts of the function f(x) = x² + 4x + 3 can be found as shown below.
f(x) = x² + 4x + 3
0 = x² + 4x + 3
0 = (x+3)(x+1)
x = -3, -1
Now, it can be seen that Mathieu has actually set the factored expressions equal to each other, which was wrong.
Hence, the correct option is C.
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I need help with this within the next /0 mins sum1 plz help
Answer: Second option.
Step-by-step explanation:
Given the function f(x), which is:
[tex]f(x)=x[/tex]
And given the function g(x), which is:
[tex]g(x)=2[/tex]
You need to substiute the function [tex]g(x)=2[/tex] into the function [tex]f(x)=x[/tex] in order to find [tex](fog)(x)[/tex].
Therefore, through this procedure, you get this answer:
[tex](fog)(x)=(2)[/tex]
[tex](fog)(x)=2[/tex]
You can observe that this matches with the second option.
For this case we have the following functions:
[tex]f (x) = x\\g (x) = 2[/tex]
We must find [tex](f_ {0} g) (x).[/tex]
By definition of composite functions we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
We substitute g (x) into f (x), then we have:
[tex]f (g (x)) = 2[/tex]
Answer:
[tex]f (g (x)) = 2[/tex]
Option B
Which angle of rotation is an angle of rotational symmetry for all figures?
Answer:
there isn't a direct answer for that because it depends on the shape.
but it has rotational symmetry if it can be rotated by an angle between 0° and 360°