Given:
Area of a triangle, A = 16 ft²
Base of the triangle, b = 4 ft
Height of the triangle, h, is unknown.
To find the height of the triangle, h, apply the formula below:
[tex]A=\frac{1}{2}b\times h[/tex]Rewrite the formula for h.
Multiply both sides by 2:
[tex]\begin{gathered} 2A=\frac{1}{2}b\times h\times2 \\ \\ 2A=b\times h \end{gathered}[/tex]Divide both sides by b:
[tex]\begin{gathered} \frac{2A}{b}=\frac{b\times h}{b} \\ \\ \frac{2A}{b}=h \\ \\ h=\frac{2A}{b} \end{gathered}[/tex][tex]h=\frac{2A}{b}[/tex]Where,
A = 16 ft²
b = 4 ft
Substitute values into the formula and evaluate.
We have:
[tex]\begin{gathered} h=\frac{2A}{b} \\ \\ h=\frac{2(16)}{4} \\ \\ h=\frac{32}{4} \\ \\ h=8\text{ ft} \end{gathered}[/tex]Therefore, the value of h is 8 ft
ANSWER:
H = 8 ft
Write the rate as a unit rate.980 cars in 280 households?
Which of the following are true about the graph of y = (x - a)(x - b)2(x - c)3I) The graph travels through the point x = aII) The graph "bounces off" the point x = bIII) The graph "bounces off" the point x = c
Consider the given equation,
[tex]y=(x-a)(x-b)^2(x-c)^3[/tex]Put x = a in the equation,
[tex]\begin{gathered} y=(a-a)(a-b)^2(a-c)^3 \\ y=(0)(a-b)^2(a-c)^3 \\ y=0 \end{gathered}[/tex]So the graph of the function passes through (a,0), which is a valid point.
So, option (I) is correct.
Similarly, when substituting the other values, it is obtained that the curve of the given function passes through points (b,0) and (c,0).
But this contradicts with the statements in (II) and (III) respectively.
Therefore, it can be concluded that only statement (I) is correct.
Identify the function shown in this graph. 5 4 3 2 과 2 பான் O A. y = x + 4 ос B. y=-x+4 C. y= x-4 D. y=-x-4
Given the graph of the line passes through the points ( -4 , 0 ) and ( 0 , 4 )
The general form of the line is : y = mx + b
where m is the slope and b is y-intercept
The slope will be calculated as following:
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{4-0}{0-(-4)}=\frac{4-0}{0+4}=\frac{4}{4}=1[/tex]b = y intercept = ( the value of y when x = 0 )
So, as the line pass through the point ( 0 , 4 )
b = 4
so, the equation of the line is:
[tex]y=x+4[/tex]The temperature was 55 degrees when i left my house this morning at 7am. At 4pm the temperature was 82 degrees. What was the percent change in temperature?
Answer:
27/55 × 100 = 49.0909090909 %
The table shows the amounts of onions and tomatoes in batches of different sizes in a sauce recipe.Elena observes that if she takes the number in the column for tomatoes and divides it by the corresponding number in the column for onions, she always gets the same result.What is the meaning of the number that Elena calculated?onions (ounces)246tomatoes (ounces)163248More about this source textSource text required for additional translation informationSend feedbackSide panels
The number that Elena calculated is the constant of proportionality, which express the ratio of two proportional quantities. In this case, it expresses how much does the amount of tomatoes vary when the amount of onions varies, this is a directly proportional relationship.
identify the type of function represented by the equation y=-3x
y = -3x is the equation of a line, with a slope of -3 and a y-intercept of 0
Drag the red and blue dots along the x-axis and y-axis to graph 8x+2y=10
Solution
Writing in the form
[tex]\begin{gathered} y=mx+x \\ \\ \Rightarrow4x+y=5 \\ \\ \Rightarrow y=-4x+5 \end{gathered}[/tex]find the difference. you nay use a number line to help you find your answer7 - (-0.9) =
7-(-0.9)
7+ 0.9 = 7.9
Number line:
Find the value of x that will make A B5x + 20А.B3x + 60x = [?]
x = 20
Using the alternate exterior angles theorem, it was stated the exterior ang
I need to know 3 equivalent expressions for the total amount of money.
we can rewrite the expression with a factor
[tex]M=5(8pd+5pd+20d)[/tex]and we can rewrite again with the other factor "d"
[tex]\begin{gathered} M=5d(8p+5p+20) \\ M=5d(13p+20) \end{gathered}[/tex]I tried everything I could to answer this question but I couldn’t get it
We need to use some properties of the kyte:
· The opposite obtuse angles are equal. In the figure, this means ∠WZY = ∠WXY
· The large diagonal bisects the angles ∠ZWX and ∠XYZ
56 ask us to find m∠XYZ. We can note that the angles ∠ZXY and ∠XZY are congruent. And we know that the interior angles of the triangle XYZ add to 180º.
m∠VXY = m∠VZY = 58º
Then:
[tex]\begin{gathered} m∠ZXY+m∠XZY+m∠XYZ=180º \\ 58º+58º+m∠XYZ=180º \\ m∠XYZ=64º \end{gathered}[/tex]The answer to 56. is 64º
57 ask us to find m∠ZWV, we can use the second property listed above. The large diagonal bisects the angle ∠ZWX. Since we know ∠ZWX = 50º, then:
[tex]\begin{gathered} m∠ZWV=\frac{1}{2}\cdot m∠ZWX \\ . \\ m∠ZWV=\frac{1}{2}\cdot50º=25º \end{gathered}[/tex]The answer to 57 is 25º
58 ask us to find m∠VZW. We know that the sum of all internal angles of a kite (or any quadrilateral), is 360º.
We know:
m∠ZWX = 50º
m∠WZY = m∠WXY
m∠XYZ = 64º
Then:
[tex]\begin{gathered} m∠ZWX+m∠WZY+m∠WXY+m∠XYZ=360º \\ 50º+2m∠WZY+64º=360º \\ 2m∠WZY=360º-114º \\ m∠WZY=\frac{1}{2}\cdot246º \\ m∠WZY=123º \end{gathered}[/tex]And:
[tex]m∠WZY=m∠VZW+m∠VZY[/tex]Now replace the known values of m∠WZY = 123º and m∠VZY = 58º:
[tex]\begin{gathered} 123º=m∠VZW+58º \\ m∠VZW=123º-58º=65º \end{gathered}[/tex]The answer to 58 is 65º
59 ask us to find m∠WZY, we sis it in 58 to find m∠VZW.
The answer to 59 is 123º
Select the correct answer from each drop-down menu.A carpenter is building a triangular frame. She has three pieces of wood measuring 5 feet. 6 feet, and 12 feet.The carpenter build the triangular frame with the three pieces of wood. She could cut the to create a triangular frame.piece byNext
Explanation
Answer:
The carpenter can build the triangular frame by cutting the 12 foot piece by 2foot
Can you help me with this question? I have no other information.
Given,
The number of lawn mowed by Thomas is 35.
The amount of tip thomas got is $150.
The number of lawn mowed by Candice is 30.
The amount of tip Candice got is $275.
They charged equal price to mow each lawn.
Consider,
The amount of mowing the one lawn is x.
According to the question,
[tex]undefined[/tex]INSTRUCTIONS: JCTIONS: e slope of the line er it here:m=1/3 Find the slope of the line and enter it here: 4 ey-intercept of & enter it Find the y-intercept of the line & enter it here: Write the equation of the line in form y=mx+b + he equation of in form y=mx +b /3x + 2 30 म
The equation of a line in the slope intercept form is expressed as
y = mx + b
where
m represents slope
b represents y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
From the graph,
When x1 = 1, y1 = - 2
when x2 = 2, y = 1
Slope = (1 - - 2)/(2 - 1) = 3/1
Slope = 3
The y intercept is the value of y at the point where the line cuts through the y axis. Thus, y intercept = - 5
To write the equation of the line, we would substitute m = 3 and b = - 5 into the slope intercept equation. Thus, the equation of the line is
y = 3x - 5
100 + (n - 2) ^ = 149 how do I solve this what is the first step??
The given expression is
[tex]100+(n-2)^2=149[/tex]First, we have to subtract 100 on each side
[tex]\begin{gathered} 100-100+(n-2)^2=149-100 \\ (n-2)^2=49 \end{gathered}[/tex]Hence, the answer is the first option, that's the first step.The reason for this first step is because we can't take a square root without getting rid of the terms 100, otherwise, the process would be wrong.
At Hayley’s Beading Boutique there are 23 plastic beads and 2 metal beads on clearance. What percentage of the beads on clearance are plastic? PLEASE ANSWER!!!
The percentage of the beads on clearance are plastic is 92%.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that At Hayley’s Beading Boutique there are 23 plastic beads and 2 metal beads on clearance.
The percentage will be calculated as,
P = 23 / 25
P = 0.92
Multiply by 100 to convert into a percentage,
P = 92%
Therefore, the percentage of the beads on clearance are plastic is 92%.
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Find the missing side length and angles of ABC given that m A = 41°, b = 4, and c = 10.
To solve this question, we would use cosine rule which is given as
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Our values have been defined for us and we will proceed to evaluate
[tex]\begin{gathered} a^2=4^2+10^2-2(4)(10)\cos 41 \\ a^2=16+100-80\cos 41 \\ a^2=116-60.376 \\ a^2=55.624 \\ \text{take the square root of both sides} \\ a=\sqrt[]{55.624} \\ a=7.458\approx7.5 \end{gathered}[/tex]From the calculations above, the value of the missing side a is 7.5 units
To find angle B,
we can use sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \frac{7.5}{\sin 41}=\frac{4}{\sin B} \\ \sin B=\frac{4\times\sin 41}{7.5} \\ \sin B=0.3498 \\ B=\sin ^{-1}0.3498 \\ B=20.5^0 \end{gathered}[/tex]We can still approach C with sine rule or sum of angle in a triangle
[tex]\begin{gathered} A+B+C=180 \\ 41+20.5+C=180 \\ c=118.5^0 \end{gathered}[/tex]From the calculations above, the value of a = 7.5 , B = 22⁰ and C = 118.5⁰ respectively which is option B
write an equation of each line shown below in slope- intercept form
Step-by-step explanation:
red: y=2x-1
blue: y=-2/5x-1
What is the inequality shown?
The inequality shown is -4 ≤ x ≤ 3.
In graph, as we can see the dots are solid that means inequality is not strict which leads to use of equal sign as well.
In graph, the line is from -4 to 3, that means the number exists between or equals to -4 and 3.
Hence, inequality is -4 ≤ x ≤ 3.
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The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 4 ft long with a diameter of 1.6 ft. Suppose gas is poured into the tank at a rate of 1.9 ft^3 per minute. How many minutes does it take to fill the empty tank?
Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Hence, the minutes it take to fill the empty tank is [tex]8.0384min[/tex].
What is the volume of cylinder?
The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold.
In geometry, there is a specific volume of a cylinder formula that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly.
Here given that,
The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is [tex]4[/tex] ft long with a diameter of [tex]1.6[/tex] ft. Suppose gas is poured into the tank at a rate of [tex]1.9ft^3[/tex] per minute.
Here,
[tex]d=1.6ft\\r=0.8ft\\h=4ft[/tex]
The general formula for the volume of cylinder is
[tex]V=\pi r^2h\\V=(3.14)(0.8)^2(4)\\V=(3.14)(0.64)(4)\\V=8.0384min[/tex]
Hence, the minutes it take to fill the empty tank is [tex]8.0384min[/tex].
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For questions 7-8: P is the center of a circle with diameter KR.7. If P(7,-5) and R(4,-2), find the coordinates of point K.8. What is the length of the radius to the nearest hundredth?
Answer:
7.) The coordinates of point K are (10,8)
8.) The length of the radius, to the nearest hundreth, is of 4.24 units.
Step-by-step explanation:
P is the center of a circle with diameter KR:
This means that P is the midpoint between K and R.
I will see that the points are:
[tex]P(x_P,y_P),K(x_K,y_K),R(x_R,y_R)[/tex]Since P is the midpoint:
[tex]x_P=\frac{x_K+x_R}{2},y_P=\frac{y_K+y_R}{2}[/tex]P(7,-5) and R(4,-2)
This means that:
[tex]x_P=7,y_P=-5,x_R=4,y_R=-2[/tex]7. If P(7,-5) and R(4,-2), find the coordinates of point K
[tex]x_P=\frac{x_K+x_R}{2}[/tex]Substituting:
[tex]7=\frac{x_K+4}{2}[/tex][tex]x_K+4=14[/tex][tex]x_K=10[/tex]Now we do the same for y:
[tex]y_P=\frac{y_K+y_R}{2}[/tex]Replacing with what we have
[tex]-5=\frac{y_K-2}{2}[/tex][tex]y_K-2=-10[/tex][tex]y_K=-8[/tex]The coordinates of point K are (10,8)
8. What is the length of the radius to the nearest hundredth?
The radius is half the diameter(distance between KR divided by 2). It can also be the distance between an endpoint of the circle and the centre(Distance between P and K, or between P and R).
I am going to calculate the distance between P and R.
P(7,-5) and R(4,-2). So
[tex]R=\sqrt{(7-4)^2+(-5-(-2))^2}=\sqrt{3^2+(-5+2)^2}=\sqrt{9+9}=\sqrt{18}=4.24[/tex]The length of the radius, to the nearest hundreth, is of 4.24 units.
what is the prescribed dosage for a 4 yr old child, if the adult dosage is 180 milligram
In order to calculate the child's dosage, let's use the value of n = 4 and M = 180 in the formula, then we calculate the value of D:
[tex]\begin{gathered} D=\frac{n}{n+12}\cdot M \\ D=\frac{4}{4+12}\cdot180 \\ D=\frac{4}{16}\cdot180 \\ D=\frac{1}{4}\cdot180 \\ D=\frac{180}{4} \\ D=45 \end{gathered}[/tex]So the child's dosage is 45 milligrams.
The container that holds the water for the football team isfull. After pouring out 5 gallons of w2gallonsХ5?
Answer:
25 gallons
Explanation:
Let's call x the number of gallons that the container can hold.
The container starts half full, so it starts with (1/2)x gallons, then they pour out 5 gallons to let the container 3/10 full, so we need to subtract 5 gallons to get (3/10)x gallons. It means that we can write the following equation
[tex]\frac{1}{2}x-5=\frac{3}{10}x[/tex]Now, we can solve the expression for x, so
[tex]\begin{gathered} \frac{1}{2}x-5+5=\frac{3}{10}x+5 \\ \frac{1}{2}x=\frac{3}{10}x+5 \\ \frac{1}{2}x-\frac{3}{10}x=\frac{3}{10}x+5-\frac{3}{10}x \\ \frac{1}{5}x=5 \\ 5\cdot\frac{1}{5}x=5\cdot5 \\ x=25 \end{gathered}[/tex]Therefore, the container can hold 25 gallons.
under which of these conditions will the law of sines not give additional information about the triangle?A. two sides and the included angle are given B. two angles and a side opposite one of them are given C. two sides and an angle opposite one of them are given
We will have that the law of sines won't give us any more information under the following situation:
*Two sides and the included angle are given. [Option A]
Louis wants to bake 10 cakes for the church festival. She needs 1 3/4cups of flour and 2 1/2 cups of sugar for each cake. How much flourwill she need for the 10 cakes?Enter your answer as an improper fraction.
Total = 10 cakes
Flour = 1 3/4
Sugar = 2 1/2
Change the fractions to improper fractions
Flour = 1 3/4 = 7/4
Sugar = 2 1/2 = 5/2
Multiply each numbher by 10
Flour = 7/4 x 10 = 70/4
Sugar = 5/2 x 10 = 50/2
Change to proper fractions
Flour = 17 1/2 cups
Sugar = 25 cups
If you toss two dice, what is the probability that the sum of the dots is either 7 or 11?
sum of 7:
there are 6 combinations: (1,6) (6,1) (2,5) (5,2) (3,4) and (4,3)
[tex]=6\times\frac{1}{36}=\frac{6}{36}[/tex]sum of 11:
there are 2 combinations: (5,6) and (6,5)
[tex]=2\times\frac{1}{36}=\frac{2}{36}[/tex]thus the probability is
sum of 7 + sum of 11
[tex]\begin{gathered} =\frac{6}{36}+\frac{2}{36} \\ =\frac{8}{36} \\ =\frac{2}{9} \end{gathered}[/tex]therefore = 22%
Hi, can you help me answer this question, please, thank you!
Given:
mean, u = 0
standard deviation σ = 1
Let's determine the following:
(a) Probability of an outcome that is more than -1.26.
Here, we are to find: P(x > -1.26).
Apply the formula:
[tex]z=\frac{x^{\prime}-u}{\sigma}[/tex]Thus, we have:
[tex]\begin{gathered} P(x>-1.26)=\frac{-1.26-0}{1} \\ \\ P(x>-1.26)=\frac{-1.26}{1}=-1.26 \end{gathered}[/tex]Using the standard normal table, we have:
NORMSDIST(-1.26) = 0.1038
Therefore, the probability of an outcome that is more than -1.26 is 0.1038
(b) Probability of an outcome that
To solve the equation 2x - 6 = 30 by balancing, what would be step?
Given the equation
[tex]2x-6=30[/tex]To solve the equation means to determine the value of x, so your objective will be to isolate the x term in one side of the equal sign.
To do this using the balancing method, you have to "pass" all unrelated terms to the other side if the equal sign by performing the oposite operation.
So, first step is to pass -6 to the other side by adding it to both sides of the equation
[tex]\begin{gathered} 2x-6+6=30+6 \\ 2x=36 \end{gathered}[/tex]Next, the x term is being multiplied by 2, to cancel this multiplication you have to divide it by 2. And, to keep the equality valid, any operation performed in one side of the equal sing must be performed on the other side so, divide 36 by 2 too.
[tex]\begin{gathered} \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]Express the answer in terms of a natural logarithm. Y= (do not simplify)
Solution
Exponential expressions with natural base e are of the form
[tex]y=a.e^{kx}[/tex]The value of 'a' is already set to be 96 since this is the coefficient of the given equation. We just need to find k
so set 3.8^x as e^kx and solve for k
[tex]\begin{gathered} 3.8^x=e^{kx} \\ 3.8^x=(e^k)^x \\ 3.8=e^k \end{gathered}[/tex]The two sides have the same exponent of x. So the two bases are 3.8 and
e^k must be equal to
[tex]\begin{gathered} e^k=3.8 \\ k=ln(3.8) \\ k=1.335 \end{gathered}[/tex]This means
[tex]e^{kx}=e^{1.335x}[/tex]and we replace the
[tex]3.8^x=e^{1.335x}[/tex]to go from
[tex]y=96(3.8)^x[/tex]to
[tex]y=96.e^{1.335x}[/tex]Therefore the correct answer is
[tex]y=96.e^{1.335x}[/tex]Two angles are supplementary angles if the sum of their measures is 180. Find the measures of two supplementary angles if the measure of one angle is 4 degrees less than three times the other.What are the measures of the two angles?
Answer:
The measures of the two angles are 46° and 134°.
Explanation:
Let x and y be the two angles:
x+y=180
It is mentioned that the measure of one angle is 4 degrees less than three times the other.
Let:
y=3x-4
Then, we substitute y=3x-4 into x+y=180.
So,
[tex]\begin{gathered} x+y=180 \\ x+(3x-4)=180 \\ \text{Simplify and rearrange} \\ x+3x-4=180 \\ 4x=180+4 \\ 4x=184 \\ x=\frac{184}{4} \\ \text{Calculate} \\ x=46 \end{gathered}[/tex]We substitute x=46 into x+y=180. So,
[tex]\begin{gathered} x+y=180 \\ 46+y=180 \\ \text{Simplify and rearrange} \\ y=180-46 \\ \text{Calculate} \\ y=134 \end{gathered}[/tex]Therefore, the measures of the two angles are 46° and 134°.