SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]5a-10b=45[/tex]STEP 2: Substitute 3 for b in the equation
[tex]5a-10(3)=45[/tex]STEP 3: Simplify the equation to solve for a
[tex]\begin{gathered} 5a-30=45 \\ 5a=45+30 \\ 5a=75 \\ a=\frac{75}{5} \\ a=15 \end{gathered}[/tex]Hence, the value of a is 15
What is the quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in
scientific notation?
The quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in scientific notation is 1.4x10^6.
What is quotient?
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is used to describe the integer component of a division (when Euclidean division), as well as a fraction or a ratio (when proper division). A quotient in the second sense is only the proportion of a dividend to its divisor.
Lets calculate the quotient for the value given in question:
[tex]7.7 \times 10^8[/tex]
[tex]5.5 \times 10^2[/tex]
Now we divide the 7.7 by 5.5
[tex]\frac{7.7}{5.5} = 1.4[/tex]
we get value 1.4.
on dividing [tex]\frac{10^8}{10^2}[/tex] we get, [tex]10^6[/tex]
Combining both the value, we get
quotient = [tex]1.4 \times 10^6[/tex]
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2(3x - 1) + 2(4x + 5) = 8
Answer:
0
Step-by-step explanation:
2(3x -1) + 2(4x + 5) = 8 Distribute the 2's
2(3x) + 2(-1) + 2(4x) + 2(5) = 8
6x - 2 + 8x +10 = 8 Combine like terms
14x + 8 = 8 Subtract 8 from both sides of the equaion
14x = 0 Divide both sides by 14
x = 0
The owners of the Movie Palace use the Illuminator 100 light bulb in their projectors, but are now considering switching to the Illuminator 100 Plus, a more powerful light bulb that projects movies onto larger screens farther away. The Illuminator 100 Plus projects movies onto screens 108 feet wide and 180 feet from the projector, while the Illuminator 100 projects movies onto screens only 81 feet wide, as shown in the figure below. How much farther from the projector, in feet, is the screen for the Illuminator 100 Plus than the screen for the Illuminator 100 ?
Given that the illuminator 100 plus bulb movies onto larger screen farther away as shown in the diagram attached then;
Illuminator 100 plus bulb
It movies onto screens ;
108 ft wide
180 ft away from the projector
Illuminator 100 bulb
81 ft wide
? : from the projector
Here apply the idea of similarity ratios where;
The ratio
Look at triangle ABC on the coordinate plane. 1 Which coordinate plane shows triangle ABC after a reflection over the y-axis?
We a figure is being reflected over the y-axis, the y-coordinates of its point will not change. However, the x-coordinates will be multiplied by -1.
Given points of the figure:
Point A: -5,-2
Point B: -4,-4
Point C: -6,-4
Let's now determine the new points of the figure once reflected over the y-axis.
Point A: -5,-2 ➜ Point A': (-5)(-1),-2 = 5,-2
Point B: -4,-4 ➜ Point B': (-4)(-1),-4 = 4,-2
Point C: -6,-4 ➜ Point C': (-6)(-1),-4 = 7,-4
Looking at the
50 points for this one
Answer:
-1, 0
Step-by-step explanation:
Hello!
We can test each solution for by substituting the value for x, and see if the inequality is true.
x = -1:[tex]\frac{3(-1)^2}{(-1)^2+3} < 1[/tex][tex]\frac34 < 1[/tex]This inequality is true.
x = -2:[tex]\frac{3(-2)^2}{(-2)^2+3} < 1[/tex][tex]\frac{12}{7} < 1[/tex]This inequality is not true because 12/7 is greater than 1.
x = 0:[tex]\frac{3(0)^2}{(0)^2+3} < 1[/tex][tex]0 < 1[/tex]This is inequality is true.
x = 3:[tex]\frac{3(3)^2}{(3)^2+3} < 1[/tex][tex]\frac{27}{12} < 1[/tex]This inequality is not true because 27/12 is greater than 1.
The solutions that work are -1 and 0.
Answer: A
Step-by-step explanation:
Find csco, cose, and tan , where is the angle shown in the figure.Give exact values, not decimal approximations.
Let 'a' represent the unknown side of the triangle.
To solve for the unknown side, we will apply the Pythagoras theorem.
[tex]a^2=b^2+c^2^{}[/tex][tex]\begin{gathered} b=4 \\ c=5 \end{gathered}[/tex][tex]\begin{gathered} a^2=4^2+5^2 \\ a=\sqrt[]{16+25} \\ a=\sqrt[]{41} \end{gathered}[/tex]Let solve for cscθ
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sin \theta=\frac{4}{\sqrt[]{41}} \\ \text{Therefore,} \\ \csc \theta=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \end{gathered}[/tex]Let us solve for cosθ
[tex]\cos \theta=\frac{5}{\sqrt[]{41}}[/tex][tex]\begin{gathered} \frac{5}{\sqrt[]{41}} \\ \text{Rationalising} \\ \frac{5}{\sqrt[]{41}}\times\frac{\sqrt[]{41}}{\sqrt[]{41}}=\frac{5\sqrt[]{41}}{41} \end{gathered}[/tex][tex]\cos \theta=\frac{5\sqrt[]{41}}{41}[/tex]Let us solve for tanθ
[tex]\tan \theta=\frac{4}{5}[/tex]Which of the following is not a solution 3x-5<2
SIMPLIFY THE EQUALITY FIRST
[tex]3x \leqslant - 2 + 5 \\ 3x \leqslant 3 \\ \frac{3x}{3} \leqslant \frac{3}{3} \\ x \leqslant 1[/tex]
X CAN BE ALL THE NUMBERS LESS OR EQUAL TO 1
IN THE PICTURE THE ONLY OPTION THAT CONTRAST THE INEQUALITY IS OPTION B BECAUSE IT IS GREATER THAN 1.
HOPE THIS HELPS
Answer:
option B
Step-by-step explanation:
3x - 5 ≤ -2
add 5 to both sides
3x - 5 + 5 ≤ -2 + 5
3x ≤ 3
divided both sided by 3 to get x alone
3x/3 ≤ 3/3
x ≤ 1
option B is the only choice that is above 1.01 making it not a solution
please help me solve,the question is A cylinder with a diameter of 8 feet is cut out of a cube that measures 8 feet on each side.What is the volume of the resulting shape? ( use Pi and round to the nearest tenth.) ______ ft3
Side of cube = 8 ft
Volume of cube = Side x Side x Side
Volume of cube = 8 x 8 x 8
Volume of cube = 512 feet^3
A cylinder with diameter 8feet is cute form the cube
Height of cylinder = Side of cube
Height of cylinder = 8 feet
Diameter of cylinder = 8 feet
Radius of cylinder = 4feet
[tex]\begin{gathered} \text{Volume of cylinder =}\Pi\times radius^2\times Height \\ \text{Volume of cylinder =}\Pi\times4\times4\times8 \\ \text{Volume of cylinder =}401.92ft^3 \end{gathered}[/tex]The volume of resulting shape = Volume of cube - Volume of cylinder
Volume of resulting shape = 512 - 401.92
Volume of resulting shape = 110.08 ft^3
Answer: 110.08 ft^3
I'm In K12" Help me Pleeasee *I Will Give "Brainlyest to The First Person"
The correct inequality sign for the first number expression is > and for the second number, the expression is <.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The mixed fractions are:
-19 5/6 = -119/6 = -19.83
-20 1/6 = -121/6 = -20.166
-19 5/6 > -20 1/6
|-19 5/6| = |-119/6| = 19.83
|-20 1/6| = |-121/6| = 20.166
|-19 5/6| < |-20 1/6|
Thus, the correct inequality sign for the first number expression is > and for the second number, the expression is <.
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the probability that the mean salary of the sample is less than $60,000 is? round 4 decimals if needed.
Answer:
0.26599
Step-by-step explanation:
We will assume a normal distribution for the salaries
We have the following information
Mean μ = 64000
Standard deviation σ = 6400
And we are asked to find P(X < 60000)
First find the z score corresponding to X = 60000
The z score is given by (X - μ) / σ
z score for 60000 with μ = 64000 and σ = 6400 is
z = (60000 - 64000)/6400
z = -40000/6400 = -0.625
We can either look up the P value from the z-tables or simply use a calculator
P(X < 60000) and this works out to 0.26599
I only need help with part "b." I have provided the answer for "a" to help.
Part b.
If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:
Factor of 3
[tex]3\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {3} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Multiply:
[tex]\begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix}[/tex]Answer:
[tex]\begin{equation*} \begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix} \end{equation*}[/tex]help me please if you can i need to know the equation
Following the instructions provided, we shall use a graphing calculator (Desmos) to determine the equation of the circle shown by the "colorful people."
The first step is to determine the radius which we can observe from the circle itself, whose diameter spans from 0 units to 10 units along the x-axis. The radius therefore is 5 units (half of the diameter).
Observe also that the center has now moved away from the origin (0, 0), and if we move the slider very carefully for h, that would be 5 units away from the origin towards the right (along the x-axis), andk would be 7 units away from the origin) towards the bottom (along the y-axis).
After following these steps, we can replicate the circle given in the question and if we now substitute the values of h, k and r into the equation of a circle, we would end up with;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Where;} \\ h=5,k=-7,r=5 \\ \text{The equation becomes;} \\ (x-5)^2+(y-\lbrack-7\rbrack)^2=5^2 \\ (x-5)^2+(y+7)^2=25 \end{gathered}[/tex]While sailing a boat offshore, Bobby sees a lighthouse and calculates thatthe angle of elevation to the top of the lighthouse is 3°. When she sails her boat700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.How tall, to the nearest tenth of a meter, is the lighthouse?
Given
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
To find:
How tall, to the nearest tenth of a meter, is the lighthouse?
Explanation:
It is given that,
While sailing a boat offshore, Bobby sees a lighthouse and calculates that
the angle of elevation to the top of the lighthouse is 3°.
When she sails her boat 700 m closer to the lighthouse, she finds that the angle of elevation is now 5°.
That implies,
[tex]\tan3\degree=\frac{y}{x+700}[/tex]Also,
[tex]\begin{gathered} \tan5\degree=\frac{y}{x} \\ y=x\tan5\degree \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \tan3\degree=\frac{x\tan5\degree}{x+700} \\ (x+700)\tan3\degree=x\tan5\degree \\ x\tan3\degree+700\tan3\degree=x\tan5\degree \\ (\tan5\degree-\tan3\degree)x=700\tan3\degree \\ 0.0351x=36.6854 \\ x=1045.7m \end{gathered}[/tex]Then,
[tex]\begin{gathered} \tan5\degree=\frac{y}{1045.7} \\ y=1045.7\tan5\degree \\ y=91.5m \end{gathered}[/tex]Hence, the height of the light house is, 91.5m.
Use 3.14 for pi or the pi button and round to the nearest hundredth. The volume of the cone?
Given:-
[tex]r=4.5,h=9[/tex]To find the volume of cone.
So the volume formula for cone is,
[tex]v=\pi r^2\frac{h}{3}[/tex]Substituting we get,
[tex]\begin{gathered} v=3.14(4.5)(4.5)(\frac{9}{3}) \\ v=3.14(4.5)(4.5)(3) \\ v=190.755 \end{gathered}[/tex]So the required solution is 190.76
without graphing, describe the transformation of each parabola or absolute value function y = 2 |x|+ 1
Remember the following transformations of a function:
[tex]c\cdot f(x)[/tex]This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0
If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1
[tex]f(x)+c[/tex]This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.
Therefore, starting with the absolute value function:
[tex]\lvert x\rvert[/tex]Multiply the function by 2:
[tex]2\cdot\lvert x\rvert[/tex]Since 2>1, then this is a vertical stretching by a factor of 2.
Next, add 1:
[tex]2\cdot\lvert x\rvert+1[/tex]This will translate the stretched absolute value function one unit upwards.
Therefore, the complete description of the transfromation would be:
[tex]y=2\cdot\lvert x\rvert+1[/tex]Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.
1. Line Q goes through (-6,7) and (4,-2). Write the equation of line Q.
First, find the slope of the line using the slope formula:
Provided two points (a,A) and (b,B) on a line, its slope is given by:
[tex]m=\frac{A-B}{a-b}[/tex]For the points (-6,7) and (4,-2), we have:
[tex]\begin{gathered} m=\frac{7--2}{-6-4} \\ =\frac{7+2}{-10} \\ =\frac{9}{-10} \\ \therefore m=-\frac{9}{10} \end{gathered}[/tex]The equation of a line in slope-intercept form, of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Substitute m=-9/10 and the coordinates of one point to find the y-intercept. Use, for instance, the point (-6,7):
[tex]\begin{gathered} 7=-\frac{9}{10}(-6)+b \\ \Rightarrow7=\frac{54}{10}+b \\ \Rightarrow b=7-\frac{54}{10} \\ \therefore b=\frac{8}{5} \end{gathered}[/tex]Substitute b=8/5 and m=-9/10 to find the equation of line Q:
[tex]y=-\frac{9}{10}x+\frac{8}{5}[/tex]Wade and Ida are salespeople who earned the same amount this week, although Ida made 4 more sales than Wade. Wade earns a base of $153 plus $22 per sale. Ida earns a base of $17 plus $24 per sale. Write the equation for the number of sales Wade made this week
Answer:
y = 24x + 17 20
Step-by-step explanation:
Firstly, let's say that 153 and 17 are both the y-intercepts of their respective equations, while 22 and 24 are the slope. With this we can create the following set of equations:
y = 24x + 17
y = 22x + 153
So your answer would be y = 24x + 17
Now let's find the sales answer!
Since we know that Ida made 4 more sales than Wade this week, we could say:
y = 24(x+4) + 17
y = 22x + 153
Now since we know that they earned the same amount we can do the following:
24(x+4) + 17 = 22x + 153
Simplify...
24x + 96 + 17 = 22x + 153
Simplify again:
24x + 113 = 22x + 153
subtract 22x and 113 from both sides...
2x = 40
Then:
x = 20
So this means that Wade made 20 sales this week!
So let's check if we are right:
Now that we know that x = 20, we need to plug it into Wade's equation!
y = 22(20) + 153
y = 440 + 153
y = 593
Wade made $593 this week!
To check if we are right, let's plug it into Ida's equation:
y = 24x + 113
y = 24(20) + 113
y = 480 +113
y = 593
Ida also made $593 this week!
MEANING we are right!
I hope I helped :P
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: .25x + 75.00 = C(x)
Step-by-step explanation:
Im not the best at word problems please help.Frank knows that his first four test grades were 74, 76, 77, and 84. Use the formula x‾=x1+x2+…+xnn to find Frank's grade on the fifth test if his test average is 80.6.
Given:
Frank knows that his first four test grades were 74, 76, 77, and 84
We will find Frank's grade on the fifth test if his test average is 80.6.
So, let the fifth grade = x,
The average is the sum of the grades over the number of the grades
So,
[tex]\frac{74+76+77+84+x}{5}=80.6[/tex]Solve the expression to find x:
[tex]\begin{gathered} 74+76+77+84+x=5\cdot80.6 \\ 311+x=403 \\ x=403-311=92 \end{gathered}[/tex]So, the answer will be: the fifth grade = 92
What is the value of sec 3pi/2 in simplest form with a rational denominator?
The given expression is
[tex]sec\frac{3\pi}{2}[/tex]Since sec is the opposite of cosine, then
[tex]sec\frac{3\pi}{2}=\frac{1}{cos\frac{3\pi}{2}}[/tex]Since the value of cos(3pi/2) is 0, then
[tex]\begin{gathered} cos\frac{3\pi}{2}=0 \\ \\ sec(\frac{3\pi}{2})=\frac{1}{cos\frac{3\pi}{2}}=\frac{1}{0} \end{gathered}[/tex]Since 1/0 is an undefined value, then
The answer is undefined
HELP ASAP WILL GET THE BRAINLEST FOR THIS ANSWER PLEASE ANSWER CORRECTLY
Answer:
(x,y)->(x+4,y-5)
Step-by-step explanation:
Find a set of common points first, for example, A and A', or B and B'
Then, find the coordinates of the two points. I'm choosing B and B'.
B: (1,8) x = 1, y = 8
B':(5,3) x = 5, y = 3
from B to B', we see that the x increases by 4 and the y decreases by 5. So, the third option, (x,y)->(x+4,y-5) is correct
I need help with this question but no one is helping me! Can someone please help me
Answer:
when rounding the answer it shouldn't be the exact answer so add or multiply then once you find your product round it off and add a decimal
State the domain and range for the graph and tell if it is a function.
The arrows indicate that the graph of the function continues beyond what can be seen in the image.
Notice that the graph does not appear to have asymptotes; then, the domain of the function is:
[tex]\text{domain}=(-\infty,\infty)[/tex]And the range is:
[tex]\text{range}=(-\infty,\infty)[/tex]Since the graph seems to continue towards the +y-direction and the -y-direction
Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; the graph is a function.
please help with this practice question, thank you
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 50.2 . You would like to be 90% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?
The required sample size of the given estimate is 3030.65.
Given that,
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/1.5]²
Substitute values in the above equation,
n = [1.645×50.2/1.5]²
n = 3030.65
Thus, the required sample size of the given estimate is 3030.65.
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If F(X) = 5x-7 and G(X)= -2x+9, what is G(F(X))?O A. -10x +23O B. -10X2 +59x-63O C. -10x+38O 10XD. 10x7 - 59x+63
f(x) = 5x - 7
g(x) = -2x + 9
g(f(x)) = -2(5x -7) + 9 = -10x + 14 + 9 = -10x + 23
g(f(x)) = -10x + 23
Answer:
Option A: -10x + 23
C IS BETWEEN A AND D, B IS THE MIDPOINT OF AC . IF BD =15 AND BC= 7, FIND AD
BD= 12
BC=7
Is this from a graded quiz?
Write an expression describing all the angles that are coterminal with 346°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)
______ degrees
Answer:
346 + 360k
You can get coterminal angles by adding intervals of 360 degrees
Maggie's brother is 3 years younger than four times her age. The sum of their ages is 42.How old is Maggie?Maggie isyears old.
The age of Maggie is 9 years and her brother whose age 3 years less than four times Maggie's age is 33 years old.
What is age?
Age is the difference in days, months, and years between the day, month, and year of birth and the day, month, and year of the event, expressed in the largest completed unit of solar time, such as years for adults and children and months, weeks, days, hours, or minutes of life, as appropriate, for infants under one year of age (Gregorian calendar).
Let the ages of Maggie and her brother be X and Y.
There are two condition given in the question through which we can form a system of equation containing two equations.
First condition: The sum of their ages is 42.
Therefore,
X + Y = 42
Second Condition: Maggie's brother is 3 years younger than four times her age.
Therefore,
4X - 3 = Y
We get the system of equation:
X + Y = 42
4X - 3 = Y
Solving this system of equation
4X - 3 = Y
4X - 3 = 42 - X
X = 45/5
X = 9
Putting the value of X in one of the equation:
Y = 42 - X
Y = 42 - 9
Y = 33
Therefore, age of Maggie is 9 years and age of her brother is 33 years.
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pls solve this question properly
Answer:
∡BOA ≅ ∡DOC
Step-by-step explanation:
Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.
CongruenceAll of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.
Corresponding parts of congruent triangles are congruent, so ...
∡BOA ≅ ∡DOC