Answer:
12
Step-by-step explanation:
g(1.5) is 8 - 3(1.5), or 8 - 4.5, or 3.5.
Then substitiute 3.5 for x in h(x) = 2x + 5: h(g(1.5)) = h(3.5) = 7 + 5 = 12
Your question asks what the value of h(g(1.5)) is.
Answer: 12To find the answer to your question, we're going to need to solve g(x) first, then plug in the answer from g(x) to h(x).
Lets solve:
We're going to plug in 1.5 to our "x" variables in the g(x) equation.
Your equation should look like this:
[tex]g(x)=8-3(1.5)[/tex]
Now, you solve:
[tex]g(x)=8-3(1.5)\\\\g(x)=8-4.5\\\\g(x)=3.5[/tex]
You should get 3.5
Once you're done solving g(x), we would plug in the answer we got from the G(x) equation into our h(x) equation.
Your equation should look like this:
[tex]h(x)=2(3.5) + 5[/tex]
Then, you solve:
[tex]h(x)=2(3.5) + 5\\\\h(x)=7+5\\\\h(x)=12[/tex]
Once you're done solving, you should get 12
This means that the value of h(g(1.5)) is 12.
12 should be your FINAL answer.
I hope this helps!Best regards, MasterInvestorWhich graph best represents the function g(x) = (x - 2)x + 4)?
Sorry if it’s kinda hard to see
Answer:
b.
Step-by-step explanation:
expand (x-2)(x+4)
(x-2)(x+4)=0
x²+2x-8=0
a=1,b=2,c=-8
From this equation we know that ,
a>0, the shape of the graph is a minimum graph.
c is the y-intercept ,the graph will intercept -8 at y-axis .
By solving this (x-2)(x+4)=0 we know the x-intercept of the graph .
(x-2)(x+4)=0
x=2 ,x=-4
There are 19 sticks of gum left in one packet, and 6 sticks of gum in another packet that are going to be split evenly between 2 people. How many sticks of gum does each person get? Choose the correct answer from the choices below.
[tex]19 + 6 = 25 \div 2 = 12.5[/tex]
Answer:
12.5
Step-by-step explanation:
19+6=25 , 25÷2= 12.5
please help!! Thanks!!
Answer:
a = sqrt(33)
Step-by-step explanation:
a^2 + 4^2 = 7^2
a^2 + 16 = 49
a^2 = 33
a = sqrt(33)
22. How many times smaller is the surface area of a sphere if the diameter is multipled by 1/4?
Answer:
4 times smaller
Step-by-step explanation:
PLEASE someone help me with maths
You are on the right tracks.
Since angle ABC is a right angle, that means lines AB and BC are perpendicular.
Therefore the gradient of BC = the negative reciprocal of the gradient of AB. We can use this to form an equation to find what K is.
You have already worked out the gradient of AB ( 1/2) (note it's easier to leave it as a fraction)
Now lets get the gradient of BC:
[tex]\frac{5-k}{6-4}= \frac{5-k}{2}[/tex]
Remember: The gradient of BC = the negative reciprocal of the gradient of AB. So:
[tex]\frac{5-k}{2} =negative..reciprocal..of..\frac{1}{2}[/tex]
So:
[tex]\frac{5-k}{2}=-2[/tex] (Now just solve for k)
[tex]5-k=-4[/tex]
[tex]-k=-9[/tex] (now just multiply both sides by -1)
[tex]k = 9[/tex]
That means the coordinates of C are: (4, 9)
We can now use this to work out the gradient of line AC, and thus the equation:
Gradient of AC:
[tex]\frac{1-9}{-2-4} =\frac{-8}{-6} = \frac{4}{3}[/tex]
Now to get the equation of the line, we use the equation:
y - y₁ = m( x - x₁)
Let's use the coordinates for A (-2, 1), and substitute them for y₁ and x₁ and lets substitute the gradient in for m:
y - y₁ = m( x - x₁)
[tex]y - 1=\frac{4}{3}(x +2)[/tex] (note: x - - 2 = x + 2)
Now lets multiply both sides by 3, to get rid of the fraction:
[tex]3y - 3 = 4(x+2)[/tex] (now expand the brackets)
[tex]3y - 3 = 4x+8)[/tex]
Finally, we just rearrange this to get the format: ay + bx = c
[tex]3y - 3 = 4x+8[/tex]
[tex]3y = 4x+11[/tex]
[tex]3y - 4x = 11[/tex]
And done!:
________________________________
Answer:
The equation of a line that passes through point A and C is:
[tex]3y - 4x = 11[/tex]
Find the value of z.
Answer:
[tex]\large\boxed{\dfrac{50}{3}}[/tex]
Step-by-step explanation:
If the polygons are similar, then the corresponding sides are in proportion:
[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex] cross multiply
[tex]12z=(10)(20)[/tex]
[tex]12z=200[/tex] divide both sides by 12
[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]
he graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. Which statement about the domain and range of each function is correct? The range of the transformed function and the parent function are both all real numbers greater than or equal to 4. The domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. The range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. The domain of the transformed function and the parent function are both all real numbers.
Answer:
Out of the four, the only statement true about the parent and the transformed function is:
"The domain of the transformed function and the parent function are all real numbers."
Step-by-step explanation:
Parent function:
f(x) = |x|
Applying transformations:
1. Stretched by a factor of 0.3:
f(x) = 3|x|
2. Translated down 4 units:
f(x) = 3|x| - 4
Transformed function:
f(x) = 3|x| - 4
We can see that:
Range of the parent function = All real numbers greater than or equal to 0.
Range of the transformed function = All real numbers greater than or equal to -4.
Domain of the parent and the transformed function is same and equal to all real numbers.
Hence, the first three statements are wrong and the fourth one is true.
Answer:
The domain of the transformed function and the parent function are both all real numbers.
Step-by-step explanation:
Stretching a function by any factor doesn't change either its domain nor its range.
Translating up or down a function changes its range. In this case, the lowest value the parent function can take is 0 when x=0; after translation, for x = 0 then f(x) = -4. Therefore,
f(x) = |x|
domain = all real numbers
range = [0, infinity)
f(x) = 0.3*|x| - 4
domain = all real numbers
range = [-4, infinity)
If f(x)=1/3x^2+5, find f(-9)
Answer:
32
Step-by-step explanation:
f(x)=1/3x^2+5
Let x = -9
f(-9) = 1/3* (-9)^ 2 +5
= 1/3 * 81 +5
= 27+5
=32
roumd 33 to the nearest 100
Answer:
Step-by-step explanation:
Trick question. Good to know.
0 is the closest 100.
33 will round to 0
Which of the following is the ratio between the number of successes and the number of possible outcomes of an event?
Which expression best estimates 6 3/4 divided by 1 1/2?
Answer:
7/2
Step-by-step explanation:
Round 6 3/4 to 7
Round 1 1/2 to 2
7 divided by 2
=7/2
cube root of y equals 4
Answer:
y = 64Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]
If f(x)=6(x-2), find f(5)
Answer:
f(5) = 6(5 - 2) = 6(3) = 18
Step-by-step explanation:
You're asked to "evaluate" f(x)=6(x-2) when x = 5.
To do this, replace both instances of x with 5: f(5) = 6(5 - 2) = 6(3) = 18
Answer:
Hence, the value of the function for f(5) is 18..
Step-by-step explanation:
Consider the provided function.
[tex]f(x)=6(x-2)[/tex]
We need to find the value of function at x = 5.
Substitute x = 5 in above function and simplify.
[tex]f(5)=6(5-2)[/tex]
[tex]f(5)=6(3)[/tex]
[tex]f(5)=18[/tex]
Hence, the value of the function for f(5) is 18.
Need helpppppppppppp
Answer:
Choice D is correct
Step-by-step explanation:
We have been given the expression;
[tex]21\leq-3(x-4)<30[/tex]
The first step is to open the brackets using the distributive property;
-3(x-4) = -3x + 12
Now we have;
[tex]21\leq-3x+12<30\\\\21-12\leq-3x+12-12<30-12\\ \\9\leq-3x<18\\\\\frac{9}{-3}\geq x>\frac{18}{-3}\\\\-6<x\leq-3[/tex]
What’s the answer help plz
9 x 5 = 45 -> total $ on Friday
99 - 45 = 54 -> total $ on Saturday
54 ÷ 9 = 6 hours
Answer:
A, B.
Step-by-step explanation:
If Matt charges $9 an hour, and he worked for 5hrs on Friday night, then that means we have to do multiplication.
So, $9x5=$45.
And then it says he babysat again on Saturday, and in TOTAL, he earned $99.
So, if he already made $45, and he has a total of $99, then we need to work backwards to figure out how much he made on Saturday.
$99-$45=$54
So, he made $45 on Friday and $54 on Saturday.
Now, we continue to work backwards and divide how much he made on Saturday ($54), by how much he charges per hour.
$54/9=6
So, Matt worked a total of 6hrs on Saturday.
Which term describes lines that intersect at 90 degrees angles
Answer:
They would be perpendicular because the lines intersect at a ninety degree angle. Hope this helps! Please mark brainliest!
Step-by-step explanation:
Follow below steps:
The term that describes lines that intersect at 90-degree angles is perpendicular. Lines that are perpendicular to each other form four angles at the point of intersection. Each of these angles is a right angle, which measures 90 degrees. This is a fundamental concept in geometry, which is a branch of mathematics dealing with properties and relations of points, lines, surfaces, solids, and higher dimensional analogues.
For example, in the context of a coordinate plane, the x-axis and y-axis are perpendicular to each other. Moreover, theorems in geometry further explain the properties of perpendicular lines, such as the fact that if a line segment is drawn joining the extremities of two equal lines which are perpendicular to a given line, the joining segment is bisected at right angles by a third perpendicular line.
Solve the given inequality. If necessary, round to four decimal places.
13^4a < 19
Answer:
The solution of the inequality is a < 0.2870
Step-by-step explanation:
* Lets talk about the exponential function
- the exponential function is f(x) = ab^x , where b is a constant and x
is a variable
- To solve this equation use ㏒ or ㏑
- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)
* Lets solve the problem
∵ 13^4a < 19
- To solve this inequality insert ㏑ in both sides of inequality
∴ ㏑(13^4a) < ㏑(19)
∵ ㏑(a^n) = n ㏑(a)
∴ 4a ㏑(13) < ㏑(19)
- Divide both sides by ㏑(13)
∴ 4a < ㏑(19)/㏑(13)
- To find the value of a divide both sides by 4
∴ a < [㏑(19)/㏑(13)] ÷ 4
∴ a < 0.2870
* The solution of the inequality is a < 0.2870
Answer:
a < 0.2870
Step-by-step explanation:
We are given the following inequality which we are to solve, rounding it to four decimal places:
[tex] 1 3 ^ { 4 a } < 1 9 [/tex]
To solve this, we will apply the following exponent rule:
[tex] a = b ^ { l o g _ b ( a ) } [/tex]
[tex]19=13^{log_{13}(19)}[/tex]
Changing it back to an inequality:
[tex]13^{4a}<13^{log_{13}(19)}[/tex]
If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].
Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].
[tex]4a<log_{13}(19)[/tex]
[tex]a<\frac{log_{13}(19)}{4}[/tex]
a < 0.2870
what is the solution set of the quadratic inequality x^2-5< or equal to 0
[tex]x^2-5\leq0\\x^2\leq5\\x\leq \sqrt5 \wedge x\geq-\sqrt5\\x\in\left\langle-\sqrt5,\sqrt5\right\rangle[/tex]
For this case we must indicate the solution of the following inequality:
[tex]x ^ 2-5 \leq0[/tex]
Adding 5 to both sides of the inequality:
[tex]x ^ 2\leq5[/tex]
We apply square root on both sides of the inequality to eliminate the exponent:
[tex]x \leq\pm \sqrt {5}[/tex]
So, we have two solutions:
[tex]x\leq \sqrt {5}[/tex]
Since it is an inequality, the sign for the negative portion is changed:
[tex]x\geq- \sqrt {5}[/tex]
Answer:
[tex]x\leq \sqrt {5}\\x\geq-\sqrt {5}[/tex]
WUCLUJ
A quadrilateral has two right angles. The measure of the third angle is 99º.
What is the measure of the fourth angle?
Answer:
81 degrees
Step-by-step explanation:
A quadrilateral has four interior angles which sum up to 360 degrees.
As we are given that two angles are right angles which means the sum of two angles will be 180 degrees and the third angle is 99 degrees.
As we know that the four angles sum up to 360 degrees.
Let A,B,C and D denote the four angles,
Then
Sum of angles = 360
A+B+C+D=360
90+90+99+D=360
279+D=360
D=360-279
D= 81 degrees
So the fourth angle is 81 degrees ..
Rewritten in vertex form please!!! Asap!!!
Answer:
vertex form: [tex]y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}[/tex]
B correct
Step-by-step explanation:
[tex]y=(x+3)^2+(x+4)^2[/tex]
[tex]y=x^2+9+6x+x^2+16+8x[/tex]
[tex]y=2x^2+14x+25[/tex]
[tex]y=2(x^2+7x)+25[/tex]
[tex]y=2(x^2+7x+\dfrac{49}{4}-\dfrac{49}{4})+25[/tex]
[tex]y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}[/tex]
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
y = (x + 3)² + (x + 4)² ← expand and simplify
= x² + 6x + 9 + x² + 8x + 16
= 2x² + 14x + 25
To obtain vertex form use the method of completing the square
The coefficient of the x² term must be 1
Factor out 2 from 2x² + 14x
y = 2(x² + 7x) + 25
add/ subtract ( half the coefficient of the x- term )² to x² + 7x
y = 2(x² + 2([tex]\frac{7}{2}[/tex]) x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] ) + 25
y = 2(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{2}[/tex] + [tex]\frac{50}{2}[/tex]
y = 2(x + [tex]\frac{7}{2}[/tex] )² + [tex]\frac{1}{2}[/tex]
What is the slope-intercept equation of the line that includes the points in The table?
Answer:
A Is the correct answer ( y = 2x - 4 )
Step-by-step explanation:
The answers listed are provided in Y= Mx + B. What this means is M = Slope and B = Y Intercept. The Y-Intercept is where the imaginary line crosses the Y axis of the graph or where x = 0. In this case the Y-Int is -4 and the slope of the graph is 2 over 1 ( A rise of two and a run of one ) in other terms it's just 2, but once you put this into the equation y = Mx + B it becomes 2x. Your final product would be y = 2x - 4
Determine which type of transformation is illustrated in the figure. If none of the listed transformations apply, choose "none of these."
Answer:
15 ounces
Step-by-step explanation:
If there is 165 ounces in 11 boxes then divide the ounces by the boxes to get the amount of ounces in one box.
Answer:
15
Step-by-step explanation:
What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?
ANSWER
The radius is 4
EXPLANATION
The given equation is:
[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]
We complete the square to get the expression in standard form:
[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]
[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]
We factor using perfect squares to get:
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]
This implies that,
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]
Comparing to
[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
The radius is r=4
A line goes through the points
(−5,−8)
and
(5,2)
. Find its slope.
Answer:
Slope is 1
Step-by-step explanation:
Rise over Run. Delta y over Delta x. -8-2/-5-5 = -10/-10 = 1
What's 17⁄12 as a mixed number?
A. 1 5⁄12
B. 1 12⁄7
C. 1 7⁄12
D. 7 1⁄2
Answer:
A
Step-by-step explanation:
17 / 12
(12 + 5) / 12
12/12 + 5/12
1 5/12
Which best describes a system of equations that has no solution?
Answer:
i think the answer is undefined
Step-by-step explanation:
Answer: 1. inconsistent, 2. infinite, 3. (4, -1), 4. exactly two solutions.
Step-by-step explanation: HOPE THIS HELPS. ;))))
What are the two solutions of x2 – 2x – 4 = –3x + 9?
the y-coordinates of the y-intercepts of the graphs of y = x2 – 2x – 4 and y = –3x + 9
the x-coordinates of the x-intercepts of the graphs of y = x2 – 2x – 4 and y = –3x + 9
the y-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9
the x-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9
The solutions of:
[tex]x^2-2x-4=-3x+9[/tex] are:
The x-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9
Step-by-step explanation:Solution to a system of equation--
A solution to a system of equation are the possible values of x that satisfy both the equation.
These are obtained by finding the x-coordinate of the point of intersection of the equations i.e. the point where the y-values is equal.
Hence, the given can be solved by finding the points of intersection of the graph:
[tex]y=x^2-2x-4[/tex] and [tex]y=-3x+9[/tex] and then taking the x-coordinate of the point.
Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line 10(10m+6)<12
Answer:
B
Step-by-step explanation:
10(10m+6)<=12
100m+60<=12 Distributive Property
100m <=12-60
100m <=-48
m <=-48/100
m <=-.48
This says values for m that are less than or equal to -.48
-.48 is between -1 and 0 so the answer is B
Graph the solution set on a number line 10(10m+6)<12
10(10m+6)<=12
100m+60<=12 Distributive Property
100m <=12-60
100m <=-48
m < =-48/100
m < =- 48
This says values for m that are less than or equal to -.48
Option B. M≤ -48
What are different notations?Four popular derivative notations include: The Leibniz notation, which has a d/dx format. The Lagrange notation, characterized by prime notation. The Euler notation, where a capital D is used.
It's just a different notation to express the same thing. On the other hand, if you want to represent the set with interval notation, you need to know the upper and lower bound of the set, or possibly the upper and lower bound of all the intervals that compose the set.
What is function notation?An equation involving x and y, which is also a function, can be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” and means that y is a function of x.
To learn more about Notation, refer
https://brainly.com/question/2147364
#SPJ2
Identify the method that will be used in solving for x.
5+x=
distributive property
multiplication property of equality
division property of equality
subtraction property of equality
Answer:
subtraction property of equality
Step-by-step explanation:
The equation in the question is incomplete, the complete equation is:
5 + x = 2
To solve this equation we have to use the subtraction property of equality, that is, if you subtract some number at both sides of the equal sign, the equation doesn't change. So:
5 + x - 5 = 2 - 5 (You must select a number which isolate x)
x = -3
And the answer is gotten.
d
ur welcome its right
Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?
Answer: [tex]945\ pixels[/tex]
Step-by-step explanation:
We know that the original photo was 800 pixels wide and the new photo will be 1,260 pixels wide. Therefore, we can find the scale factor.
Divide the width of the new photo by the width of the original photo. Then the scale factor is:
[tex]scale\ factor=\frac{1,260\ pixels}{800\ pixels}\\\\scale\ factor=\frac{63}{40}[/tex]
The final step is to multiply the height of the original photo by the scale factor calculated.
Therefore the height of the new photo will be:
[tex]h_{new}=(600\ pixels)(\frac{63}{40})\\\\h_{new}=945\ pixels[/tex]
Answer:
945 pixels.Step-by-step explanation:
Givens
The original photo dimensions are (800 wide x 600 high )pixelsThe new photo is 1,260 pixels wide.First, we need to find the scale factor by dividing
[tex]s=\frac{1260}{800}=1.575[/tex]
Then, we multiply the height by the scale factor
[tex]600 \times 1.575 = 945[/tex]
Therefore, the new height is 945 pixels.